.. —...-n F}: . _ ALLIANCE F. PAYOF AND .FECIS» 0 EF 7‘ THE ATIVE STRENGT “ .. UELATIVE CONFLICT N OFREL HS A no \ SITUATIONS on THE EXTENTOF TRIBU DIS hoop-Emmh; .r/ 1. .52”, “..1 r7 . ., .t... .u J....Xi O MICHIGAN STATE UNIVERSITY; , a w . e;0f Ph D re POOLE“: Thesis :for the Bag “STEVEN ., . ,. . . , . .. , .. ‘ V! r. . . 1 M. ;. \\\\\\\\\\\\\\\\\\\\\\\\\\\II\I\I\\\\I 3 1293 10390 4961 LIBRARY Michigan State University 5555 2:: THESIS This is to certify that the thesis entitled UELATIVE CONFLICT: THE EFFECTS OF PAYOFF, DISTRIBUTION OF RELATIVE STRENGTHS, AND ALLIANCE SITUATIONS ON THE EXTENT OF COOPERATION presented by Steven G. Cole has been accepted towards fulfillment of the requirements for Ph.D degree inmgy Major professor Date JUIY 2]. I970 0—169 I ”731% ABSTRACT UELATIVE CONFLICT: THE EFFECTS OF PAYOFF, DISTRIBUTION OF RELATIVE STRENGTHS, AND ALLIANCE SITUATIONS ON THE EXTENT OF COOPERATION BY Steven G. Cole The present paper focuses on an examination of uelative conflict. Uelative conflict is defined as the contention between n-participants in an attempt to obtain incompatible positive payoffs, in a situation that is structured such that it is not necessary for any participant to receive a positive payoff and in which at most one participant may receive a positive payoff. A truel--a three person duel--was employed to test a model of uelative conflict which has been prOposed by Cole and Phillips (l969), to examine strategy preferences in a potential uelative conflict situation, and to examine both the effect of trust and a parity vs. equal division of the payoff in potential uelative conflict situations in which alliances are allowed. Six representative situations from the ' disparity of relative strengths continuum which included the all equal situation, a situation in which one player had veto power, and a situa- tion in which one player had dictatorial power were examined. The data indicated that the Cole and Phillips model offers a reasonably good approximation of strategy selection in the truel; however, the model did not offer a good fit by strict statistical criteria. Some modification of the model were suggested but no modifications were tested with the data. The potential uelative conflict condition indicated that merely inserting a means for terminating a uelative conflict situation by cOOperative behavior would not reduce the level of conflict behavior. It was pr0posed that restricted communication and the need to trust all of one's Opponents resulted in the low level of c00perative behavior. The results of the alliance games supported that assumption and suggested that trust is also an important variable with reSpect to the prOpensity to form alliances. If it is necessary to trust your alliance partner-- if your alliance partner is not forced to honor the alliance--there is a prOpensity to play the game without forming an alliance. if trust is not a variable, alliances are formed. Gamson's (l96la) prOposal that, because of a parity norm, each participant in a coalition formation situation would attempt to maximize the prOportion of the resources that he contributed to a coalition so that he would be better able to bargain for a larger share of the payoff, was tested by including rules governing the division of the payoff which negated the need for bargaining. In one condition (coali- tion parity), alliances were allowed and the alliance partners divided the alliance's share of the payoff prcportionate to their assigned strength. Those data were compared to data from a condition in which the alliance partners divided the alliance's share of the payoff equally (coalition 50/50) as well as to the combined Vinacke and Arkoff (l957) and Chertkoff (I966) data for those situations in which one player was strong, one of medium strength, and one weak, and in which any alliance had complete control of the outcome. In the coalition parity condition, weak alliances--alliances between the medium strength and weak players--were formed in virtually every case. A significantly stronger prOpensity to form weak alliances in the coalition parity condition than in the combined Vinacke and Arkoff and Chertkoff studies suggested that the subjects in the Vinacke and Arkoff and Chertkoff studies did not base their partner preferences on a strong expectation of the parity norm. It was suggested that the parity norm might be Operating in coalition formation situations, but that its effect is not as strong as the effect of the parity division of the payoff in the present experiment. A significant prOpensity to form either strong alliances-~alliances between the strong and medium strength players-~or weak alliances was noted in the coalition 50/50 condition. Caplow's (l968) suggestion that partner preference might be a function of the subjective prOpinquity of the labels associated with each player was eXpanded to include the subjective prOpinquity of the strength associated with each player and proposed as an eXplanation of the non-random partner preference observed in the coalition 50/50 condition. e . . ..fl ,. /)// // , Approved by 47//U‘/ r/ {)ji’MIJ/f” V, Date 7/1/ :2. l K/ 3’75) Committee James L. Phillips, Chairman William D. Crano John T. Gullahorn Mark E. Rilling UELATIVE CONFLICT: THE EFFECTS OF PAYOFF, DISTRIBUTION OF RELATIVE STRENGTHS, AND ALLIANCE SITUATIONS ON THE EXTENT OF COOPERATION By Steven 61 Cole A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Psychology 1970 Q,— 0550 .3 /'»e9..;1~‘"// ACKNOWLEDGEMENTS The author wishes to eXpress his sincere appreciation to Dr. James L. Phillips for his criticism and advise prior to and during the preparation of this thesis. Equally sincere appreciation is extended to the author's wife Betty for her patient support, her love, and the many hours she spent preparing the final manuscript. The effort extended by my collegues E. Alan Hartman and Gary Mendelsohn in preparation of the computer programming and designing and building the experimental apparatus are appreciated more than it is possible to eXpress. Appreciation is also eXpressed to the members of the author's committee; Dr. William Crano, Dr. John Gullahorn, and Dr. Mark Rilling. Finally, the author's sincere appreciation is extended to his eXperimenters Al Baume, Bob Daley, Stephen Doty, and Mike Frampton. The present research was supported by an NSF improving doctoral dissertations grant (6502825) and a grant from the Air Force Office of Scientific Research (F4h620-69-C-Ollh). TABLE OF CONTENTS PAGE LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . IV LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . vii INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . I Truel Research . . . . . . . . . . . . . . . . . . . . 6 PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . I6 METHOD. . . . . . . . . . . . . . . . . . . . . . . . . . . 30 RESULTS AND DISCUSSION. . . . . . . . . . . . . . . . . . . 47 A Test of the Cole and Phillips Model. . . . . . . . . 47 Potential Uelative Conflict. . . . . . . . . . . . . . 82 CONCLUSION. . . . . . . . . . . . . . . . . . . . . . . . . 124 LIST OF REFERENCES. . . . . . . . . . . . . . . . . . . . . I27 APPENDIX. . . . . . . . . . . . . . . . . . . . . . . . . . I30 TABLE IO II l2 LIST OF TABLES D(A), 0(8), and D(C) for the Six Game Types. Type, Number, and Order of Games Played by Each Triad. Mean Probability of Attacking the Stronger Opponent and Standard Deviations for Player Position, Game Type, and Session Number . . . . . . . . . . . . . . Summary of Analysis of Variance on Attack Data Summarized in Table 3 . . . . . . . . . Mean Probability of Attacking the Stronger Opponent in the Pure Truel and Standard Deviations for Player Position, Game Type, and Pre and Post Potential Uelative Conflict. . . . . . . . . . . . . Summary of Analysis of Variance on Attack Data Summarized in Table 5. . . . . . . . . Predicted and Observed First Trial Attacks and P (Attack) on the Stronger Opponent. Observed and Estimated n for Players A, B, and C Attacking Their Stronger Opponent in Game Types 7/6/5 through il/6/l on Trial l. . . . . . . Summary of Analysis of Variance on n for Players A, B, and C in Game Types 7/6/5 through ll/6/l . Summary of Duncan's Multiple Range Test on Mean n's for Players A, B, and C. . . . Summary of Duncan's Multiple Range Test on Mean n's for Game Types 7/6/5 through lI/6/l. Estimated n, Observed and Predicted Attacks on the Strong Opponent, and the P(Attacking the Strong Opponent) for Players B and C in the 6/6/6 through lO/6/2 Game Types (Trial 1).. . . PAGE 3] A6 A9 50 5A 55 58 60 6O 6i 6i 66 TABLE PAGE l3 Computed n and Estimatedn for Players A, B, and C on Trials Following Trial l in Game Types 6/6/6 through ll/6/l . . . . . . . . . . . . . . . . . . . . . 69 lh Predicted and Observed Attacks on the Stronger Opponent and P(Attacking the_Stronger Opponent) for Player Position and Game Type on Trials Following Trial 1. . . . . . . . . . . . . . . . . . . . 7l 15 Correlation Coefficients and Chi-Squares Comparing the Attack Data Across Trials, Within Game Types and Player Positions . . . . . . . . . . . . . . . . . . 75 I6 Observed and Predicted Frequencies of Survival and of No Player Surviving . . . . . . . . . . . . . . . . . 76 l7 Probability of Passing Score for Player Position and Game Type. . . . . . . . . . . . . . . . . . . . . . 84 I8 Summary of Analysis of Variance on Data in Table l7 (ll/6/l Included). . . . . . . . . . . . . . . . . . . . 85 I9 Summary of Analysis of Variance on Data in Table I7 (II/6/l Excluded). . . . . . . . . . . . . . . . . . . . 85 20 Summary of Duncan's Multiple Range Test on Data in Table 17 (ll/6/I Excluded) . . . . . . . . . . . . . . . 87 2| Contacts in the Initial Contact Period in the 7/6/5, 8/6/4, and 9/6/3 Alliance Games. . . . . . . . . . . . . 88 22 Alliances Resulting from Initial Contacts in the 7/6/5, 8/6/h, and 9/6/3 Alliance Games . . . . . . . . . 89 23 Initial Contacts for Each Player Position in the l0/6/2 and ll/6/l Mutual Defense and Non-Aggression Games. . . . . . . . . . . . . . . . . . . . . . . . . . 93 2h The A8, AC, and BC Alliances Resulting from Initial Contacts in the lO/6/2 and ll/6/l Mutual Defense and Non-Aggression Games . . . . . . . . . . . . . . . . 9A 25 Number of Contacts Made by the Strongest Player. . . . . 96 26 Summary of Analysis of Variance on Data in Table 25. . . 96 27 Initial Contacts for Each Player Position in the l0/6/2 and ll/6/I Coalition (SO/50) and Coalition (Parity) Games . . . . . . . . . . . 98 TABLE PAGE 28 The A8, AC, and BC Alliances Resulting from Initial Contacts in the iO/6/2 and ll/6/l Coalition (Parity) and Coalition (50/50 Games . . . . IOO 29 Probability of Attacking Given an Opportunity to Attack . . . . . . . . . . . . . . . . . . . . . . l02 30 Summary of Analysis of Variance for P (Attacking/Opportunity) . . . . . . . . . . . . . . . lO3 3l Mean Number of Attacks Per Game . . . . . . . . . . . l05 32 Summary of the Analysis of Variance on Mean Number of Attacks Per Game. . . . . . . . . . . . . . lO6 33 Mean Number of Attacks Per Game for Game Type and Conflict Type, Collapsed Over Player Position and Alliance Type . . . . . . . . . . . . . . . . . . . . lO7 3% Probability of Survival . . . . . . . . . . . . . . . IO9 35 Summary of Analysis of Variance on P (Survival) Data . . . . . . . . . . . . . . . . . . . llO 36 Distribution of Alliances as Reported by Vinacke and Arkoff (I957), Chertkoff (I966), and the Coalition (Parity) and Coalition (50/50) Conditions in the Present Study . . . . . . . . . . . ll9 vi FIGURE I0 LIST OF FIGURES Overhead view of the experimental apparatus . (Plate l) Peripheral Experimental Apparatus . (Plate 2) Peripheral Experimental Apparatus . Mean Probability of Attacking the Stronger Opponent and Standard Deviations for Player Position, Game Type, and Session Number . Mean P(attacking the stronger opponent) in the pure truel for game type and player position. Mean P(attacking the stronger Opponent) in the pure truel for game type and player position in the pre and post potential uelative conflict games. . The number of reflective cycles (n) and the best fit linear approximation to n for players A, B and C in game types 7/6/5 through ll/6/l and for players B and C when the II/6/l game type is excluded (Trial I) . . The probability of players A, B, and C attacking their stronger Opponent for all six game types (Trial 1) o o o o o o o o o o o o o o o o O The probability of players B and C attacking their stronger Opponent for game types 6/6/6 through I0/6/2 (Trial I). . . . . . . . . . . . . . . The probability of players A, B, and C attacking their stronger Opponent for all six game types (Trial 2) o o o o o o o o o o o o o o o o o o o The probability of players A, B, and C attacking their stronger Opponent for all six game types (Trial 3) . . Observed and predicted P(survival) and P (no survivor) for the pure truel. . vii PAGE 33 34 35 A9 52 56 63 6h 67 72 73 77 “War is a Species of conflict: consequently, by understanding conflict we may learn about the probable characteristics Of war under different conditions and the methods most suitable for regulating, preventing, and winning wars.” (Wright, l95l, p. I93) The above quotation by Quincy Wright would seem to reflect the reasons that in the past twenty years there has been a prodigious amount of scholarly effort directed toward understanding conflict. One tack of the examination of conflict has focused on describing conflict behavior by means of mathematical models. Within the frame- work of mathematical models some scholars (e.g., Richardson, l960a, I960b) have chosen to examine case studies of conflict as it has occurred in the real world, while others (e.g., RapOport, l967, I968) have chosen to examine experimental simulations of conflict. Richardson (l960a) considered the process of action and reaction from which wars deveIOp, with a focus on armament races. He also attempted to quantify the measureable relations between conflicting social units such that they could be interpreted statistically (Richardson, l960b). In short, Richardson Offered an exhaustive survey of historical data associated with conflict situations. There are scholars; however, who question the feasibility of examining conflict through case studies due to the many uncontrolled variables involved. These scholars tout the merits of rigidly con- trolled laboratory experiments and have studied the behavior of individuals in games designed to include the possibility of conflict behavior. Prominent among the scholars who have chosen to use games to examine conflict in the laboratory is Anatol RapOport who prOposes that a I'degree of realism” is an essential feature of game research designed to examine conflict (RapOport, I967). This realism may range from a complex facsimile of an imagined situation in intricate detail to those games which remove all but the essential features that have been marked for special attention. RapOport suggest that the intricate detail found in the complex experiment results in difficulty in both interpretation and replication. Moreover, he states that “if the aim Of research is to construct some sort of theory of conflict and of conflict resolution, a theory based. . on an analysis of controlled and repeatable situations, then one is forced to strip the situation to barest essentials” (p. A). The paradigm which has resulted from stripping the situation to the barest essentials is the 2 x 2 matrix game--a decision situation in which each of two players has a choice between two strategies. RapOport and Guyer (I966) have restricted the utilities (payoff preferences) associated with each subject to an ordinal scale and have enumerated 78 non-equivalent 2 x 2 matrix games.l With few exceptions (e.g., Deutsch and Krauss, I962; Shure, Meeker, and Hansford, I965; Sermat and Gregovich, I966; Ellis and Sermat, I968) research concerned with examining conflict in two person 1Two games are considered to be equivalent if the payoff matricies are identical after one or any combination of the follow- ing transformations: (I) interchanging rows; (2) interchanging columns; (3) interchanging players. All other games are considered to be non-equivalent. (RapOport and Guyer, I968) laboratory games has concentrated on only one of these 78 games-- the prisoner's dilemma game (RapOport and Chammah, I965). In the prisoner's dilemma game each player has two strategy choices and the payoff is determined by both players. Should both players cooperate, they each get their second most preferred payoff. Should one player defect and the other COOperate, the defector gets his most preferred payoff and the COOperator gets his least preferred payoff. Should each player defect, both players receive their third most preferred payoff. One of the attractions of the prisoner's dilemma as an ex- perimental paradigm is the fact that it is a well controlled situation in which the dependent variable--the number of cOOperative responses by each subject--is easily quantifiable. In addition it has been considered to be a semi-realistic situation in which the players make decisions and bargain as they would in real life. There are situations, however, in which the prisoner's dilemma encounters difficulties. Foremost among them is the difficulty which arises when an attempt is made to design replicable and interpretable experi- ments using the prisoner's dilemma paradigm in conflict situations involving more than two participants. The n-uel (an n-person duel) (Cole and Phillips, I969; Cole, Phillips, and Hartman, in preparation) overcomes the dyadic restriction placed on the prisoner's dilemma while it retains those aspects which are considered to be desirable. Any conflict situation in which 'n' participants contend for incompatible positive payoffs, in which it is not necessary that any of the participants receive a positive payoff, and in which at most one of the participants may receive a positive payoff, is defined as an n-uel. The contention between participants in an attempt to obtain a positive payoff is defined as ”uelative conflict” (Cole and Phillips, I969). A simple example of the pure uelative conflict situation is a duel-to-the-death which has two possible outcomes; either one partici- pant wins and the other loses or both participants lose. Since uelative conflict is exemplified by a duel-to-the-death, it follows that an incompatibility Of goals is present in uelative conflict situations. Conflict resulting from such an incompatibility of goals has been considered pure conflict by Shelling (l963), Boulding (l963), and Coser, (I969). The incompatibility of goals does not imply a zero sum or even a constant sum situation. It does imply a situation in which at most one party can achieve its objective. Uelative conflict is unique in that all parties may fail to obtain their objective. A somewhat less extreme form of uelative conflict is exemplified by a duel in which the negative payoff involved is not necessarily death. For example, consider a duel In which a wound or a unilateral refusal to participate is sufficient to discontinue the conflict. In such a situation it is still the case that the goals of the partici- pants are incompatible. However, the availability of a divisible payoff structure associated with the situation increases the number of possible outcomes (Phillips and Nitz, I968; Nitz and Phillips, l969); thus, increasing the number of possible strategies which may be employed. The defining factor--that at most one participant can receive a positive payoff--remains. Moreover, it remains possible for all of the players to lose. Although it Is doubtful that pure uelative conflict has ever existed between nation states, it can be argued that certain states of affairs (for example, war) bear a strong resemblance to it. The spectre Of two or more nuclear powers involved in an altercation is an example of uelative conflict of colossal and terrifying prOportions. The state of the world at present readily allows us to visualize such a situation. We are confronted with a potential three-nation duel between the United States, Russia, and China. All have nuclear capabilities and all see their goals as incompatible. Fortunately faced with such a situation it is usually possible to find alternatives that mediate the situation. The problem is one of negotiation and bargaining which includes limited war (Shelling, I963) and hopefully will not inevitably result in uelative conflict (nuclear war). Since the possibility of uelative conflict is present, the salient question is: Is there some means by which a potential uelative con- flict situation can be transformed into a cooperative situation rather than a pure uelative conflict situation? That is, what factors contribute to the contention that has been defined as uelative conflict? The present study utilized a three person n-uel, termed a truel by Shubik (l96h), to examine pure uelative conflict, potential uelative conflict, and some possible means for transforming a potential uelative conflict situation into a COOperative situation. The purpose of the present study was threefold. First it tested a model of uelative conflict prOposed by Cole and Phillips (l969); second, it examined the strategies employed in a potential uelative conflict situation; and third, it examined some aSpects of the interpersonal behavior exhibited when alliances between participants are allowed in the potential uelative conflict situation. Truel Research There has been an effort in recent years to develOp laboratory simulations of uelative conflict (Willis and Long, I967; Cole and Phillips, I967; Cole, Phillips and Hartman, in preparation). The focus of these efforts has been the truel. The truel paradigm was first discussed by Shubik (l95h) and was based on the concept of a three person duel. In a duel, two opponents attempt to eliminate each other and the winner is the one who survives. The truel is a similar situation which differs only in that there are three Opponents. Shubik proposed a theory to account for the outcome of the truel which was based on the presupposition that the participants in a truel will act rationally, that is, without fail each participant will attack the Opponent which Offers the greatest threat to his survival. One of the major predictions of Shubik's theory was that given a slight disparity of relative strengths the ”strongest" participant will be functionally the weakest and the ”weakest” participant will be functionally the strongest. The present paper will refer to this phenomenon as a ”power inversion” effect (Cole, I969). To illustrate his theory, Shubik offered the following example. Person A, person B, and person C are each allowed to attack one of the other two. Person A has an 80% chance Of eliminating the person that he chooses to attack, person B has a 70% chance of eliminating the person that he chooses to attack, and person C has a 60% chance of eliminating the person that he chooses to attack. The rationalistic point of view assumes that each individual wishes to survive and will, therefore, attack that individual who poses the greater threat to his survival. Shubik adopted this point of view and computed the probability of survival for each individual in each of the six possible attack orders. The following mean chance of survival for each individual was Obtained: A = .260, B = .h88, and C = .820. It is apparent that in this example the strongest person has the least chance to survive and the weakest person has the best chance to survive. Thus, the rationalistic point of view leads to the expectation of a power in- version effect in some truel situations. Shubik noted, however, that there are situations in which the strongest participant in a truel has the best chance for survival and suggested that the power in- version effect is a function of the relative strengths of the partici- pants in the truel. Thus, Shubik reasoned that ”in a non-cOOperative environment it apparently does not pay to be slightly stronger than the others for this invites action against oneself” (p. 45). Several studies (Willis and Long, I967; Cole and Phillips, I967; Cole, I968, I969; Hartman and Phillips, I969; Phillips, Hartman, and Klein, I970; Phillips, Klein, and Hartman, I970; Hartman, I970a; Hartman, I970b; Cole, Phillips, and Hartman, in preparation) have examined the truel situation. Although the Willis and Long study utilized the truel paradigm, the players were all of equal strength and an examination of the power inversion effect was impossible. Cole and Phillips (I967) examined a truel situation in which A > B >»C, i.e., player A had greater strength than player B and player 8 had greater strength than player C. They reported that: (I) player A was attacked a significantly greater number of times by both players 8 and C than either players B or C were attacked by each other, and (2) player C was attacked significantly less by players A and 8 than players A and B were attacked by each other. Thus, the hypothesis that each participant in a truel will attempt to eliminate the person that offers the greatest threat to his survival was supported; however, the strongest Opponent was not attacked with probability one as Shubik prOposed. Unfortunately, Cole and Phillips did not examine a pure truel situation. In the truel situation which they examined the players were allowed to communicate and enter into common fate alliances. The formation of common fate alliances made it impossible to examine the power inversion effect with respect to relative chance for survival. Cole (I968, I969) examined the pure truel situation in which A > B > C, and replicated the Cole and Phillips (I967) results with respect to the prOpensity to attack the stronger and weaker attack choices. When the relative chance for survival was examined; how- ever, the power inversion effect was not observed. The data suggested that a revision of Shubik's theory was in order. Cole (I968) Offered the following theory to explain individual behavior within the truel as well as the outcome of the truel. The basic assumption of the theory prOposed by Cole (I968) was that truel situations are ordered along a continuum which is based on the disparity of relative strengths. Strength was defined as the differential ability of an individual in the truel to control the outcome of the situation. The proposed continuum extended from those situations in which all three participants in the truel are equal in strength to those situations in which one member Of the truel has complete control, i.e., one member has dictatorial powers. It was predicted that the power inversion effect, i.e., the propensity to attack the stronger man and refrain from attacking the weaker man, would appear in the interpersonal interaction within the truel as long as the relative strengths were not equal. Moreover, as the disparity of relative strengths increases, the power inversion effect becomes stronger. The increases in the power inversion effect continues until it reaches its maximum strength at that point on the continuum at which the strongest member of the truel has complete control of the situation, I.e., the dictator point. At no point on the continuum will a prOpensity to attack the weaker of the two attack choices be observed. Cole (I968) prOposed that, although it is obviously dependent upon the preferred attack choice, the power inversion effect with respect to relative chance for survival in the truel is different from the power inversion effect for preferred attack choice. At that point on the continuum at which all participants are of equal strength, they each have an equal chance for survival, i.e., no power inversion effect occurs. However, as the disparity of relative strengths increases the power inversion effect (as observed in the probability that the strongest member of the truel will survive) becomes more likely. At a point on the continuum, prior to the dictator point, the strongest player has enough relative strength to permit him to partially control the outcome. That point is designated the partial control point. At the point immediately preceding the partial control point the power inversion effect reaches its maximum strength. Between the partial control point and the veto point the power inversion effect decreases due to the fact that the strongest member of the truel is in a position which allows him to partially overcome the attacks of the other members of the truel. At the dictator point the strongest member has complete control over the outcome and he will survive. Hartman and Phillips (I969), Phillips, et. al. (I970), and Hartman (l970b) have concentrated on comparing single parameter mathematical models which attempt to predict behavior in the truel. The parameter that they consider to be most relevant to such behavior is the probability of attacking the stronger Opponent which they assumed to be invariant across the disparity of relative strengths continuum. Their models are restricted to situations in which the participants are equal except for the resource dimension describing the physical assets of the participants. In some cases the models have resulted in predictions which are reasonable approximations of the observed behavior; however, the assumption that the probability of attacking the stronger Opponent does not vary regardless of relative strength is questionable, and the restriction to situations in which only one resource dimension is varied limits the generalizability of the models. On the other hand, Cole and Phillips (I969) and Cole, Phillips, and Hartman (in preparation) have offered a model of behavior in uelative conflict situations which considers multiple resource dimensions and which proposes that the probability of attacking the stronger Opponent is a function of the disparity of relative strengths. A description of the experimental paradigm for examining the truel which was used by Cole and Phillips (I967) and Cole (I968, I969) is presented below to simplify an explanation of the Cole and Phillips (I969) and Cole, Phillips, and Hartman (in preparation) model. The paradigm employs three persons as subjects or participants in a simple game which can easily be generalized to an n-person game. In II the game, each participant is assigned a number of markers or points, as well as a certain capability for destroying the markers of his opponents. The Object of the game is for each player to retain some of his markers after his opponents' markers have been completely destroyed. If there are 'n' players in the game, there are n + l possible outcomes: 'n' outcomes in which one player wins and one outcome in which all players lose. Since there are three players in the truel, there are four possible outcomes: three outcomes in which one player wins and one outcome in which all players lose. For the Cole, et. al. model the resources of each player are broken down into four independent resource dimensions. The first dimension, the damage that Player X can inflict on any player given he successfully attacks another player is designated D(X). In terms of the game paradigm discussed previously, D(X) is the number of markers that Player X can destroy in a single turn. The second dimension, the probability that Player X will be successful in launch- ing his attack is designated L(X) and is assigned to each player at the beginning of each game. L(X) and D(X) combined constitute the Offensive capability of Player X. The remaining two resource di- mensions constitute the defensive capability of Player X. The first of the defensive resource dimensions, the resources controlled by Player X that determine the number of successful attacks he can survive is designated R(X). In the previously mentioned paradigm, R(X) refers to the number of markers that Player X has at any given time. R(X) decreases when Player X has been successfully attacked. The last resource dimension, I(X) is the probability that Player X will be able to intercept an attack that is directed at him; thus, rendering I2 the attack unsuccessful. I(X) is assigned to each player at the beginning of each game. In the laboratory simulation employed by Cole (I968, I969) and Cole and Phillips (I967), subjects played the game for a number of turns or trials until at least two of the three players were eliminated. Although in such an extended form of the truel, it may be necessary to conduct several trials to determine the outcome, the model which has been proposed by Cole, et. al. treats each trial as a game in normal form, that is, each trial is treated as if it were a game in itself. Where it is relevant however, the number of moves that a participant will last if he is attacked by one of the other participants is used by the model. To simplify presentation of the model, Cole et. al. defined two more variables which are a function of the four resource dimensions. The first variable S(X,Y) is the probability that Player X success- fully completes an attack on Player Y. S(X,Y) is determined by multiplying the probability that Player X successfully launches an attack by the probability that Player Y does not intercept the attack. The second variable n(X,Y) is the expected number of attacks it would take for Player X to eliminate Player Y. To determine n(X,Y) the ratio of R(Y) to the damage which Player X can inflict on Player Y (D(X)) times the probability that Player X will successfully inflict the damage on Player Y (S(X,Y)) is computed. The attack predictions of the model are based on the assump- tions that the threat of each player to each of the other players is a function of the four resource dimensions. To determine the threat of Player X to Player Y the following assumptions were made. First, l3 it was assumed that a factor which is referred to as the vulnerability of Player X to Player Y (V(X,Y)) is inversely prOportional to the number of moves it takes for Player Y to eliminate Player X, that is, as the number of moves it takes for Player Y to eliminate Player X increases the vulnerability of Player X to Player Y decreases. Second it was assumed that the attack potential of Player X to Player Y (A(X,Y)) was equal to the product of the damage that Player X could do to Player Y times the probability that he would successfully inflict the damage. Next, it was assumed that the threat of Player X to Player Y is directly prOportional to the attack potential of Player X to Player Y and the vulnerability of Player Y to Player X. Thus, as A(X,Y) increases, the threat of Player X to Player Y increases. In addition, as V(Y,X) increases T(X,Y) increases. On the other hand, the threat Of Player X to Player Y is inversely proportional to the vulnerability of Player X to Player Y. As V(X,Y) increases, T(X,Y) decreases. Thus: T(X,Y) = A(X,Y) V(Y,X) V(X,Y) The model predicts that each person will consider the con- tribution to the total threat against him which is associated with each of the other participants, and that the probability of attack- ing a given participant varies directly with the prOportion of the total threat contributed by that participant. For example, the probability that Player X will attack Player Y is directly prOportional to the ratio of the amount of threat Player Y poses to Player X to the total threat to Player X. Thus, in a truel composed of Players X, Y, and Z, the probability that Player X will attack Player Y is IA equal to the threat of Player Y to Player X divided by the threat of Player Y to Player X plus the threat of Player 2 to Player X. T(Y,X) P(X.Y) = T(Y,X) + T(Z,X) At this point the model is subject to the criticism that it oversimplifies the situation considerably. Realizing the apprOpriate- ness of this criticism and the fact that the prOposed determination of the threats overlooks some of the cognitive processes present within the situation, Cole, et. al., extended the model to include the sub- jective probability of being attacked as it is employed in the selection of attack choice. That is, the extension of the model in- corporates the subjective probability of being attacked into the determination of the threat. Thus, the threat as determined previously was designated the simple threat and the associated probabilities of attack were designated the simple probabilities of attack. The once revised threat of Player X to Player Y was defined as the product of the simple threat Of Player X to Player Y times Player Y's subjective probability of being attacked by Player X. To determine the subjective probabilities of attack, Cole, et. al., assumed that for any player, X, the subjective probability Of being attacked by any other player, Y, is equal to the objective probability with which X will attack Y. Thus, they assumed that each player expects perfect reciprocation Of attacks between himself and any other player. Using the subjective probability of attack made it possible to compute the revised threats and the associated predicted prob- abilities of attack. Next, the model was extended based on the l5 assumption that the process by which the threats were revised once was applicable for 'n' revisions. The rational for such an extension was the ascription of an active reflection process to the participants in a uelative conflict situation. The reflection process modifies the subjective probabilities of attack which in turn modifies the threats, thus, resulting in revised attack probabilities. The revised prob- abilities of attack, although dependent upon the revised threats, are eXpressed in terms of the simple threats. The general formula for predicting the probabilities of attack given 'n' reflective cycles is: 2n To(v,x) Pn(X,Y) = 2n 2n To (Y,X) + TO(Z,X) Problem As has been stated previously, the present study utilized a truel game to examine pure uelative conflict, potential uelative con- flict, and some possible means of transforming a potential uelative conflict situation into a COOperative situation. The game used in the present study was a modification of one of the games used by Cole, Phillips, and Hartman (in preparation). One player was strong, one player was of medium strength, and one player was weak (A > B > C). All three players began each game with 20 points and a zero probability of intercepting an attack. The probability of launching an attack was assigned a value of one for each of the three players. The damage that each player could do was chosen such that six different points from the all equal point to the dictator region on the diSparity of relative strengths continuum were examined. Since it was considered to be an important case, the situation in which one player had veto power was one of the points that was examined. In the pure truel games the sole survivor was considered to be the winner. The payoff for winning the game was IOO points. As in previous research, if there was no sole survivor, there was no winner and none of the participants received a payoff for that game. In the potential uelative conflict games, it was made possible for three, two, one or none of the participants to win by including a means for ending the game by COOperating. If more than one player remained at the end of the game, the IOO points payoff was divided according to the rules governing that particular condition. Two additional variables on which the present study focused were: l6 I7 (I) the level of involvement which the subjects maintained during the eXperiment and (2) the degree to which the subjects understood the rules of the game. Both of the above mentioned variables have been discussed frequently in criticisms of research which has dealt with elementary processes of interpersonal attraction and interaction in highly controlled laboratory eXperiments. Games per se have been touted as a naturally involving experiemce for the subjects. To increase the involvement many game studies have also Offered monetary rewards. It appears intuitively obvious that the competition inherent in games coupled with a monetary reward would enhance the subject's involvement in the game. There still remains the criticism directed at the subjects level of understanding of the game. This criticism has been attacked by designing experiments in which the subjects play several games or in which one game lasts several moves. Unfortunately, it appears that as the length of the game increases the degree of involvement decreases because of boredom. The present study attacked the problem of involvement and under- standing by hiring the subjects at student labor wages ($l.50 per hour) plus bonuses. The subjects participated in the experiment for 2 At the end of each six hours of three hours each day for Ih days. game playing the subject in each triad who had accumulated the most points received a bonus payment for six hours of work at $l.50 per 2All of the triads began the experiment by playing 60 of each of the six game types as a pure truel to instill an understanding of the rules of the game as well as the power associated with each player position. l8 hour. Thus, for each six hour period, the player in each triad who had accumulated the most points received double salary-~he was paid for six hours of work at $3.00 per hour. The other two players in each triad were paid for six hours of work at $l.50 per hour. A Test of the Cole and Phillips Model. Two aspects of the Cole and Phillips (I969) and Cole, Phillips, and Hartman (in preparation) model were tested by the present study. First, the probability of attack predictions for each player position were compared to the observed probabilities of attack for the six points on the disparity Of relative strengths continuum that were examined. Since Cole, et. al., considered each turn or trial within a game as independent, the predicted probabilities of attack were also compared to the observed probabilities of attack for each trial. Second, the predicted survival frequencies associated with each player position were generated for each of the six points on the diSparity of relative strengths continuum and were compared to the observed survival frequencies. Cole, et. al., considered 'n' to be invariant across the disparity Of relative strengths continuum. The present paper questions this assumption, and prOposes, instead, that 'n' varies as a function of the disparity of the strengths of a participant's attack alterna- tives. It is sensible to assume that a player whose attack alterna- tives are similar in strength would require more reflective cycles to determine his attack choice than a player whose attack alternatives are very different in strength. An increase in the disparity Of the strengths of a participant's alternatives increases the saliency of the difference between those attack alternatives, thus requiring l9 fewer reflective cycles to make a decision concerning which Opponent to attack. For the present study the relationship between the diSparity Of relative strengths and the number of reflective cycles was considered to be an inverse-linear relationship. If the above reasoning is correct, 'n' for the medium strength participant (n8) should be smaller than 'n' for either of the other two participants (nA or nc) and nA and nc should be similar. Such a prediction follows from the fact that, by definition, the medium strength participant in a truel must decide between two attack alterna- tives which are more dISparate in strength than the attack alternatives of either of the other two participants. Thus, the medium strength participant would require fewer reflective cycles to decide on his attack choice than either of his two Opponents. Since the disparity of the strengths of A and C's attack alternatives are equal, it should also be the case that nA = nc. Hypothesis l: nB nA = nc of relative strengths continuum that were examined Thus, it was hypothesized that: for the six points on the disparity in the present experiment. Potential Uelative Conflict. As was mentioned above, the potential for uelative conflict exists whenever the goals of the social units included within the situation are perceived by those social units to be incompatible. However, in the real world, such a situation does not inevitably result in uelative conflict. In real world uelative situations it is possible for all participants to refrain from contention. In such cases the contention termed uelative conflict in the present paper may never materialize. Thus, in the real world there are many potential uelative conflict situations which do not 20 enter into the uelative conflict stage due to the realization by all participants that they risk their existence by contending. For example, consider the potential three nation truel discussed previously. What factors keep Russia, China, and the United States from engaging in nuclear war? A glance at the foreign policies of the nations involved indicates that one of the major reasons that nuclear war has not been declared is that, due to a relative balance of power, none Of the nations feel that they could “win” such a war. Hopefully the relative balance of power is not the only reason that nuclear war has not been declared; however, at present it seems to be a major reason. Unfortunately, the balance of power theory seems to be focused on merely making it undesirable to engage in active contention. It does not encourage COOperation. One possible means of focusing the participants in a potential uelative conflict situation toward cooperative behavior is to persuade them to redefine their goals such that they are not incompatible. In a gaming situation such a task does not require much effort. One merely has to change the rules of the game so that whether each participant achieves his goal or not is not a function of whether the other participants achieve their goals. In the real world a redefinition of the goals is more difficult. Whereas, in the experimental game goals are usually defined materi- allstically, in the real world goals are both material and ideological. In the present experiment the monetary goals were not redefined in the potential uelative conflict situation. It was still the case that only one member of the triad could receive the bonus for each six hour period. However, the rules were modified such that the 2l participants could choose either to enter into pure uelative conflict or to refrain from conflict. If they chose to refrain from conflict they divided the IOO point payoff for the game in direct proportion to the ratio of the number of points each had remain- ing when the game ended to the total number of points remaining. Such a manipulation parallels the real world in that cooperating helps to obtain one goal while it endangers the other. For example, should Russia, the United States, and China choose to cOOperate on some economic venture they may very well eXperience a material gain. At present, however, it seems that the mere fact that they OOOperated would weaken their chances of obtaining their ideological goals. To allow the game to end by COOperative behavior each of the participants were given an Option to pass rather than attack one of the other players on each trial.3 Moreover, the game could end with three, two, one, or no survivors depending on the participants choice of strategies. Willis and Long (l967) found that once all participants had passed for two consecutive moves, in virtually all instances they continued to pass until the game ended. Thus, in the present study if at any time all surviving participants passed for three simultaneous consecutive trials the game ended. The payoff was structured such that all survivors divided a lOO point payoff in direct prOportion to the ratio of the number of points that they had remaining when the game ended to the total points 3All of the triads in the eXperiment played 30 of each of the six game types as a pass option game immediately following the 60 pure truel games. 22 remaining. The monetary reward which was paid to the player who had accumulated the most points at the end of each six hour period remained indivisible. Thus, the choice of a cooperative response (to pass) could result in raising ones own point total at the expense of raising the other survivor or survivors' point totals. Moreover, Since it required cOOperation from all surviving players to end a game by passing, it was necessary to trust that the other player or players would also pass. The confounding of immediate and long range goals was designed to make the participants in the game carefully consider the conditions under which they would prefer to pass; thus, sharing the IOO point payoff. It was predicted that the prOpensity to pass would be an inverse function of the disparity of relative strengths for two reasons. First, as the strengths become less diSparate it becomes more difficult for the participants to predict who will survive in a pure uelative conflict situation. Second, as the strengths of the participants become less diSparate the possibility of sharing the IOO points equally becomes more acceptable to all concerned. Hypothesis 2: The prOpensity to pass increases as the disparity of relative strengths decreases. Alliances in the Potentia} Uelative Conflict Situation. Consider a potential uelative conflict situation in which one partlclpant is eliminated and the remaining participants choose to pass for three simultaneous consecutive times, thus, sharing the IOO point payoff for that game. It could be said that the survivors had formed an implicit alliance. To form such an alliance the participants must have overcome the fact that communication prior to the commitment 23 to a strategy was unavailable. There is also some amount of trust necessary to continue such an alliance strategy once it has been reciprocated by the other participant. Willis and Long (l967) found that once all participants had passed for two consecutive moves, in virtually all instances they continued to pass until the game ended. This would imply that some degree of trust was present. However, Willis and Long's paradigm was unique in that the partici- pants had a retaliatory capability. Moreover, each participant had the power to eliminate any other participant with one attack. The combination of the total destruction and retaliation capabilities controlled by each participant made passing a desirable strategy. It was fairly simple to coordinate, since the likelihood of surviving once one had made an attack was low. Willis and Long found that in almost all cases, once an attack was made all participants were eliminated. The retaliatory capability virtually eliminated the need for trust. It was not necessary to trust that a participant would not attack because retaliation simply cancelled any advantage he might gain. A glance at the paradigm for the present experiment reveals that such was not the case. In fact in many instances in which only two players are remaining it is the case that should one pass and the other attack, the attacker gains such that he has complete control over the outcome of the game. Thus, he can obtain the entire IOO point payoff rather than share it. The present experiment examined the effect of trust on alliance formation by allowing explicit alliances to form prior to the attack 2h periods.“ In one condition (the non-aggression condition) the alliance partners were not allowed to attack each other at any time. If the isolate (the participant not in the alliance) was eliminated, the game ended, and the alliance partners divided the IOO point payoff in direct proportion to the ratio of the total points they had remaining to the total points remaining. In another condition (the mutual defense condition) the alliance partners were not allowed to attack each other while the isolate had points remaining; however, once the isolate was eliminated the alliance partners had the Option to attack each other. If they chose not to attack for three simul- taneous consecutive moves, the game ended and the lOO point payoff was divided as it was in the non-aggression games. Thus, both the non-aggression and mutual defense games could end in an identical manner. In the non-aggression games the subjects were forced to honor their alliance while in the mutual defense games each alliance member had to trust his partner not to attack once the isolate was eliminated. Moreover, in many cases, should one alliance member pass and the other attack, the attacker would gain complete control of the outcome. This latter situation has been classified as a terminal coalition formation situation by Caplow (I959). Caplow predicted that in such a situation no alliance would form. It seems that such a prediction is unnecessarily pessimistic and that trust might very well be triumphant. Thus, it was predicted that subjects would initially trust each other and that alliances would be formed. Whether alliances continued to be formed would be a lIAll groups played 30 of each of the six game types as an alliance game immediately following the pass Option games. 25 function of the propensity for the alliance members to refrain from attacking each other once the isolate was eliminated. If the alliance members revealed a prOpensity to attack, the formation of alliances would cease. Otherwise, alliances would continue to be formed. Since in the mutual defense games the alliance members had the Option to attack each other once the isolate was eliminated, the formation of an alliance between the two weaker players would insure each of the alliance members that their partner could do the minimum amount of damage once the isolate was eliminated. For example, consider a game in which one player is strong (A), one of medium strength (8), and one is weak (C) and in which any alliance could win. Should B and C form an alliance and A be eliminated, both B and C would be in the alliance in which the number of points that their partner could remove was minimized. Should B or C form an alliance with A however, and should the isolate be eliminated, both B and C would be in the alliance in which the number of points their partner could remove was maximized. As a result in the mutual defense games, it was predicted that there would be a tendency to form alliances between the two weaker players given that such an alliance would win. On the other hand, in the non-aggression games, once the isolate was eliminated, the game was over and the amount of the pay- off which each alliance member received was a function of the total points that he had remaining. If the weakest participant is the isolate, the least damage can be done to each alliance member and each would eXpect to receive a greater share of the payoff than if the strongest participant were the isolate. Thus, in the 26 non-aggression games, it was predicted that a prOpensity to form strong alliances would follow from the desire to minimize losses suffered from attacks by the isolate. The immediately preceding predictions only fit those games in which the distribution of relative strengths is located between the all equal point and the veto point on the disparity of relative strengths continuum. At the all equal point a random propensity to form alliances was predicted. Since at the veto point and above any winning alliance includes the strongest participant, the strongest participant was predicted to be the preferred alliance member. At the veto point the strongest participant was predicted to prefer the weakest participant and alliances composed of the strongest and weakest participants were predicted in the mutual defense games. In the non- aggression games, alliances were predicted between the strongest and medium strength participants in an attempt to minimize possible losses from attacks by the isolate. In the dictator situation it was predicted that regardless of the fact that the strongest participant was the preferred alliance partner, few alliances would form because the strongest participant had no need to form an alliance. Hypothesis 3 and A apply only to those situations between the all equal point and the veto point on the dISparity of relative strengths continuum. Hypothesis 3: In the non-aggression games, the stronger of each player's Opponents is the preferred alliance partner. Hypothesis A: In the mutual defense games the weaker of the two Opponents is the preferred alliance partner. 27 Hypotheses 5, 6, and 7 apply only to those situations at the veto point and above on the disparity of relative strengths continuum. Hypothesis 5: In both the non-aggression and mutual defense games both of the weaker players prefer the strongest player as an alliance partner. Hypothesis 6: At the veto point the strongest player prefers to form an alliance with the weakest player in the mutual defense games and with the medium strength player in the non-aggression games. Hypothesis 7: In the dictator situation the strongest player will choose not to form an alliance; thus, there will be a prOpensity not to form alliances in the dictator situation. Gamson (l96la) prOposed that each participant in a coalition formation situation would attempt to maximize the prOportion of the resources that he contributed to a coalition while at the same time entering into a winning coalition (minimum resource theory). Gamson suggested that such behavior resulted from the parity norm-~“any participant will expect others to demand from a coalition a share of the payoff prOportional to the amount of resources which they contribute to the coalition” (Gamson, l96la, p. 376). By maximizing one's share of the resources contributed to a coalition, one would be in a better position to bargain for a larger share of the payoff. In general, the research on coalition formation has tended to support minimum resource theory (e.g., Vinacke and Arkoff, I957; Gamson, l96lb; Phillips and Nitz, I968). The present experiment made a direct test of minimum resource 28 theory. In one condition (the coalition 50/50 condition) the coalition's share of the payoff was divided equally by both members of the coalition. Thus, no advantage in bargaining position could be gained by forming that coalition to which one contributed the most resources. Another condition (the coalition parity condition) was designed such that each coalition member's share of the payoff was in direct prOportion to the number of points that he could remove as compared to the total number of points that the coalition could remove. In effect, the members of the coalition were forced to divide the payoff according to the parity principle and an advantage was gained by forming that coalition to which you contributed the most resources. If minimum resource theory is correct, the participants in the coalition (SO/50) games would have no basis for determining which coalition to form, and a random preference for coalitions would be predicted. Moreover, in the coalition (parity) games, a propensity for weak coalitions would be predicted. Since coalition research to date has uncovered no reasons to believe minimum resource theory to be grossly inaccurate, the present author predicted results consistent with minimum resource theory. Hypotheses 8 and 9 apply only to those situations between the all equal point and the veto point, since they are the only games which are included within the boundary conditions of minimum resource theory. Hypothesis 8: A prOpensity to form weak coalitions will be manifest in the coalition (parity) games. Hypothesis 9: Random formation of coalitions will be manifest in the coalition (50/50) games. 29 Hypothesis IO, II, and l2 apply only to those situations at the veto point and above on the dISparity of relative strengths continuum. Since such situations fall outside of the boundary conditions of minimum resource theory, they cannot be considered a test of the theory itself. On the other hand, an application of the parity principle at the veto point and above does result in some rational predictions. Hypothesis IO: In both the coalition (50/50) and coalition (parity) games the strongest player is the preferred alliance partner of both of the weaker players. Hypothesis ll: At the veto point the strongest player prefers to form an alliance with the weakest player in the coalition (parity) games and has no preference in the coalition (SO/50) games. Hypothesis I2: In the dictator situation the strongest player will choose not to form an alliance; thus, there will be a propensity not to form alliances in the dictator situation. Method Subjects. The subjects for the experiment were 2A male students at Michigan State University. They were recruited by an advertisement in the school newSpaper which offered work between the fall and winter terms at a rate of $l.50 per hour plus bonuses. Game Design. The game was played by three players. For ex- perimental purposes the labels VAF, ZEJ, and YOV were counter- balanced over number of points to be removed and randomly assigned to the subjects for each game. Although, Hartman (l970a) found label effects in the all equal condition, subsequent research (Cole and Hartman, in preparation) has indicated that those éffects do not continue given other cues. For the present explanation of the game design the player positions were labeled A, B, and C. Each of the players began each game with 20 points (R(A) = R(B) = R(C) = 20). The probability of launching an attack (L(X)) equaled I.O and the probability of intercepting an attack (I(X)) equaled 0.0 for all players in all games. The rules of the game required that each player remove a given number of points (D(X)) from one of the other two players on each move. D(X) was varied from one game to another as indicated in Table I; however, D(X) remained constant during any given game. The removal of the points was referred to as an attack. After all three players had made their attack choices, the number of points that each player had remaining (R(X)) was calculated and the resulting information was made aVailable to all Of the players. At no time was a player's attack Choice known before every player had made his attack choice; thus, 30 3l Table l. D(A), D(B), and D(C) for the Six Game Types* Game Type Player Position I 2 3 A 5 6 D(A)= 6 7 8 9 IO II D(B)= 6 6 6 6 6 6 D(C)= 6 5 A 3 2 I *Note.--D(A), D(B), and D(C) were chosen such that the disparity of relative strengths continuum was examined from the all equal point to the dictator region. 32 the moves in the game were simultaneous. If, when the score was calculated, R(X) < O for any player, he was no longer in the game and the remaining players were required to attack each other. The winner of each game was that player who had points remaining when the other players had none. He was the sole survivor. In the cases in which none of the players had points remaining, there was no sole survivor and there was no winner. Apparatus. The subjects played the games in an 83' x I6' room which was surrounded on three sides by a U-shaped viewing room. One way mirrors and an intercom allowed the experimenter to keep a constant surveilance on all of the activity in the experimental room. Figure l presents a tOp view of the placement of the experimental apparatus. A table divider was used to minimize variance as a result of face-to-face interaction. It was designed to divide a 23' X 65' table into three sections so that the subjects could not see each other. A picture of the table divider is presented in Figure 2a. Each subject had a communication terminal located directly in front of him in his section of the table divider. The communication terminal is pictured in Figure 2b. In the upper left hand corner of the communication terminal was a green ready light which indicated when the subject could make an attack or contact choice. Three lights above the labels allowed the experimenter to communicate information to the subjects concerning which player he was during any game. Three switches below the labels allowed the subjects to indicate their attack choice and when applicable their alliance choice. A red error light in the upper right hand corner of the communication terminal flashed when the subjects made an unacceptable choice. 33 ENTRANCE L. I'I SCOREBOARD COMMUNICATION TERMINALS I I__ .____. L.__J SI S2 TABLE DIVIDER LCA Figure I. MASTER CONTROL PANEL Overhead view of the experimental apparatus. 2a Table Divider 2b Communication Terminal Figure 2. (Plate l) Peripheral Experimental Apparatus I _. wt.“ ’ . 2c Scoreboard 2d Master Control Panel Figure 2. (Plate 2) Peripheral Experimental Apparatus 36 A scoreboard which contained information concerning R(X), D(X), . and the contact or decision period number was located eight feet in front of the subjects. Figure 2c is a picture of the scoreboard as seen by the subject in the middle section of the table divider. On the right hand side of the labels, three rows of twenty lights indicated R(X) for the respective player positions. A sequence of four white and one blue light was used to facilitate computation of R(X) by the subjects during a game. D(X) for each player position was displayed by a rear screen projector immediately to the left Of the labels. Information concerning the number of the current contact or decision period was displayed immediately to the left of D(X) for the middle row on the scoreboard by means of a rear screen projector. Each digit projected by the rear screen projector was approximately A” X 23”. A Laboratory Control Apparatus (LCA) which consists of solid state logic circuits wired to a 32 X 50 programmable MAC panel (Mendelsohn, in preparation) was the central control apparatus for the experiment. The LCA was programmed to provide the experimental manipulations which were applicable at any given time. It also calculated R(X) after every trial and controlled the display of R(X) on the scoreboard. In addition, the LCA provided the power supply for the peripheral apparatus used in the eXperiment. The eXperimenter had access to a master control panel which is pictured in Figure 2d. On the left hand side of the master control panel (left of the vertical white line) were three rotary switches which controlled the label associated with each of the player positions in the table divider. For each player position three toggle switches 37 located directly below the labels were used to communicate information concerning which players had formed alliances, if any had formed. Three toggle switches located between the player positions on the 'Y' could be set so that if either of the player positions adjacent to the arm of the 'Y' on which the switch was located attacked the other player position adjacent to that arm Of the 'Y', the LCA detected an error and turned on the appropriate error light. Across the tOp right hand side of the master control panel (right of the verticle white line) were three rotary switches with which the eXperimenter set D(X) for each player. Directly below those rotary switches were three toggle switches which allowed the experimenter to disable or enable any or all player positions. In the tOp right hand corner of the master control panel was a switch which enabled the thirty second timer used to time the decision and contact period. The number of the decision or contact period was controlled by the rotary switch in the lower right hand side of the master control panel. The scoreboard power switch was located directly below the timer switch, and the switch to reset the LCA at the beginning of each game was located directly below the scoreboard power switch. A three by three who-to-whom matrix was located in the lower central region of the right hand side of the master control panel. Three red lights forming the upper left to lower right diagonal of the matrix indicated whether an error had been made. The rest of the matrix was a series of blue lights forming a standard who-to-whom matrix which revealed each player's attack or contact choice to the experimenter. Directly under the right hand column of the who-to-whom matrix was a calculate button which was used to enable 38 the subjects' control boxes at the beginning of each trial during a game. Immediately to the left of the who-to-whom matrix was a column of four lights. Directly below the four lights was a start switch. The lower three lights were green ready lights, one for each player position. The ready lights indicated to the experimenter that the position had been enabled. The top (yellow) light (the experimenter's ready light) indicated that the LCA had completed calculating R(X) and the next trial could begin. The LCA did not calculate R(X) until the experimenter had pushed the calculate switch. Special IBM scoring sheets were used to keep a lecord of who had attacked whom, who had contacted whom, and who had passed for each trial of each game. In addition the winner of each game was recorded. Samples of the scoring sheet for each of the six game types are shown in Appendix. Procedure. Eight triads participated in the experiment. Each subject was assigned to a triad such that he worked during a time period that he preferred. In addition, care was taken to insure that none of the subjects within a given triad knew each other. Each triad remained intact for IA three hour game playing sessions. Six three hour sessions were played each day between 6:00 AM and l2:OO midnight. None of the groups played more than one session during any day and three days between game playing sessions was the maximum for any group. Due to the time required to run the experiment, five trained experimenters were employed; however, all instructions were read to the subjects by the same eXperimenter. The method of presenting the instructions combined with the distance imposed by the viewing room 39 arrangement and the control of the eXperiment by the LCA, resulted in a minimal amount of interaction between the eXperimenters and the subjects. Thus, no attempt was made to counterbalance or randomize for experimenter effect. Instead both the subjects and the experimenters were assigned to time slots that they preferred. paper When the subjects applied for the job as advertized in the news- they were given the following mimeographed job description. “If you accept the job your work assignment will be to participate as a subject in a research project. This will consist of playing a game or more realistically playing variations of the same game several hundred times. The game which you will play is called a truel. A truel is defined as a three person duel, i.e., three peOple play the game and one at most can win. It is possible for no one to win the game. You will play the truel game for approximately three hours each day. There will be approximately 20 games played every hour and the winner of each game will receive IOO points. The losers (all three players in those games which no one wins) will receive no points. Your Opponents in the game will remain the same for all of the games that you play. At the end of every six hours the number of points that you have accumulated will be totaled. The person in each triad who accumulates the most points in that six hours will receive payment ($l.50 per hour) for the actual time he spent playing the game plus a bonus of an additional $l.50 for the same number of hours. Thus, the person who accumulates the most points will receive a payment of $3.00 per hour for his time for those six hours. The peOple who receive the second and third most points will receive payment of $l.50 per hour for the actual time spent playing the game but they will receive no bonus for that six hour period. At the present time it appears that you will work for three hours a day for fourteen days. The nature of the job will require that you do not miss any of the scheduled work periods unless there is an emergency. It will not be possible to allow any deviation from the schedule, since the absence of one of the players would make it impossible to play the game and would waste the other two players time for that day. If it is absolutely necessary to miss a session, advance notice which would A0 allow the session to be rescheduled would be necessary. The scheduling for the entire time that you work for us will be done before you first play the game. We will need you to participate for approximately IA days and if you are selected for the job and agree to work we will eXpect you to remain until the job is over. If you do not plan to remain for the duration of the job we would appreciate the withdrawal of your offer to work before we begin to play the games. At a later date, more specific instructions on how the truel game is played will be given to those of you who are selected for and accept the job.” Those subjects that agreed to participate in the eXperiment were aSked to indicate the hours that they preferred to work during the week. Sixty-four subjects agreed to participate at the time of the initial interview. The subjects were later contacted according to the time slots that they preferred and the order in which they had answered the advertisement. At this time the subjects that agreed to participate were told that they would not be paid until their part of the experiment was finished, and that if they did not finish the eXperiment, they would not receive any payment for the time that they had spent. This was tempered somewhat by an agreement on the part of the experimenter to consider special cases which might be caused by emergencies. In reality no emergencies occurred and all of the subjects that started the experiment finished the eXperiment. Once the 2A subjects needed for the experiment had been selected the others who had answered the advertisement were contacted and informed that they would not be needed. When the subjects first entered the laboratory they were given a quick tour of the experimental rooms to reduce any effect associated with the remote surveillance procedure. They were then seated at the table divider and read the following instructions. Al ”As you are all aware, you will be playing a game which is known as a truel. There will be approximately three hours of game playing every day and approximately 20 games played every hour. The winner of each game will receive IOO points and the losers will receive nothing. As it will be eXplained later, it is possible for all three players to lose in any game. Remember that the person who accumulates the most points during each of the seven six hour periods will receive double time pay ($3.00 per hour) for the time he spends playing the game. The other two players will receive payment for their game playing time at $l.50 per hour. The truel game which you will play is a fairly simple game. Each player will begin each game with 20 points which will be indicated on the scoreboard in front of you. On each move of the game each player will be required to remove a given number of points from one of the other two players. The number of points that each of the players will be required to remove will be indicated here on the scoreboard (point at the proper spot on the scoreboard). The number .Of points that each player may take away will remain the same throughout any given game, however, it may change from one game to the next. To facilitate scorekeeping the three players will be labeled VAF, ZEJ, and YOV. To determine which player you will be for each game you merely have to look at the three lights above the player labels on the communication terminal in front of you. You will be the player that correSponds to the light on the communication terminal. Thus, if the light above ZEJ is on you will be ZEJ, if the light above VAF is on you will be VAF, and if the light above YOV is on you will be YOV. These labels will be randomly assigned for every game so that the same player may not have the same label for two games in a row. For example, you may be ZEJ in game number I and YOV in game number 2 or ZEJ in game number I and VAF in game number 2. It is possible, moreover, that you may be ZEJ in game number I and ZEJ in game number 2. You will be given a short period of time between each game to become familiar with the attack power associated with each player for the next game as well as the position that you will play during that game. In game number I, ZEJ will remove ___points, VAF will remove ___points, and YOV will remove ___points. With one exception you must remove all of the points that you are empowered to remove on each move. The exception to the rule occurs when the player from whom you choose to remove points has fewer points than you are required to remove. In this instance, you may take all of the points away from that one player, however, you are still not permitted to take points away from the other player on that move. To indicate which A2 player you wish to attack you will press the button switch on the communication terminal in front of you. The correct button switch will be located on the communication terminal directly beneath the name of the player you wish to attack. You may not attack yourself at any time. If you do accidently attack yourself, the error light in the upper right hand corner of your communication terminal will come on momentarily. If this happens you should make another attack choice as if nothing has happened. When you have made an acceptable attack your ready light will go out. Since you may not attack yourself, you will each have two attack choice possibilities on each move. Do not try to attack both of your possible attack choices on one move. This will merely cause a delay of the game and will serve no useful purpose. When the ready light in the upper left hand corner of your communication terminal comes on, your communication terminal is functioning and you may indicate your attack choice. When all three players have made their attack choices the score- board will display the points that each player has remaining after those attacks have been recorded. The ready light will then come on again and the process will be repeated until at most one player has points remaining. All points that are removed are taken out of the game and do not belong to any of the players. If a player has no points remaining when it is time to make an attack choice he will not be allowed to participate in the game. If one player is eliminated the other two players must attack each other on every move. Thus, it is a matter of simple arithmetic to determine how the game will end once one player is eliminated. If the two remaining players eliminate each other on the same move there is no winner. If one of the two remaining players eliminates the other and has points remaining, he is the winner. The winner is the player who has points remaining when the other players' points are gone, that is, he is the sole survivor. If there is no sole survivor, there is no winner. Are there any questions? Since the ratio of the hours you work to the amount of pay you receive for each six hour period depends on your winning as many points as you can, and since the other two members of this group are your Opponents in any contention for the bonus, it should be obvious that it is to your advantage not to discuss the game with each other. Even if this is not obvious, we request that you do not discuss the game with each other at any time.” The subjects were informed about whether they had won the bonus for any particular six hour period immediately preceding the beginning of A3 the next six hour period. The information concerning who had won the bonus was known only by the subject that won. The other subjects only knew that they did not win. After 360 pure truel games were played the pass option games began. Prior to the pass Option games the subjects were read in- structions which informed them of the changes in the rules of the game. (See Appendix for these instructions). The pass Option games were different from the pure truel games in one major respect. A decision period, 30 seconds in length, was incorporated into the game. There were seven decision periods per game. During each decision period each player was allowed to attack or not to attack. No player could attack more than once in any given decision period. The attack choices were recorded on the scoreboard at the end of each 30 second decision period. If no attack was made by each player for three decision periods in succession, the game was ended. Thus, there could be three, two, one, or no survivors depending upon the play of the game. In the pass Option games the lOO point payoff was divided in direct prOportion to the number of points remaining in that game. After I80 pass Option games had been played the alliance games began. The alliance games were identical to the pass Option games in procedure with the insertion of three 30 second contact periods which preceded the seven decision periods allowed for attacks. During these three 30 second contact periods alliances could be formed. Contact choices were made by using the same button switches that were used to indicate attack choices. Each player was allowed only one contact choice during each contact period and reciprocal choices were a AA prequisite for an alliance in all of the alliance games. As soon as a reciprocal contact occurred, the alliance process ended. If there was no reciprocal contact during the three contact periods, the game was played as a pass Option game. Triads l and 2 played l80 non-aggression alliance games. They received apprOpriate instructions prior to beginning that segment of the eXperiment. (See Appendix for those instructions) A non-aggression alliance dictated that the members of the alliance could not attack each other. It did not dictate that they had to attack the third player. If the third player was eliminated, however, the game was over and the payoff was divided in direct proportion to the points each of the surviving players had remaining relative to the total points remaining. It was possible for one member of the non- aggression alliance to be eliminated and for the other member to receive all of the points. Since the pass Option was in effect, it was also possible for the members of the non-aggression alliance to pass, resulting in three survivors. When that happened the payoff was distributed as it was in the same situation in the pass Option games. Triads 3 and A played l80 mutual-defense alliance games. They received apprOpriate instruction prior to beginning this segment of the experiment (See Appendix for those instructions). The only requirement of a mutual-defense alliance was that should the third player attack one of the members of the alliance, the alliance partner of that member had to attack the third player on the following move. The members of a mutual defense allianCe were allowed to attack each other once the third player was eliminated; however, they could not A5 attack each other prior to the elimination of the third player. The procedure for the distribution of the payoff was identical to the procedure in the non-aggression alliance games. Triads 5 - 8 played l80 coalition games. They received apprOpriate instructions prior to beginning this segment of the experiment. (See Appendix for these instructions) If a coalition was formed the game was played exactly as it was in the pass option games. The only change resulting from a coalition was the rule for distributing the payoff. Since a coalition was a common-fate alliance, if at least one member of the coalition survived, they both received a payoff which was distributed according to a pre-arranged decision. If neither of the members of the coalition survived, then the coalition's share of the payoff was zero. For Triads 5 and 6 the coalition's share of the payoff was divided equally between the members (50/50). For Triads 7 and 8 the coalition's share of the payoff was divided directly proportional to the number of points that each of the coalition members could remove relative to the total points the coalition could remove (parity). Since the pass option was in effect, the members of a coalition could choose not to eliminate the third player.~ In such a case the share of the payoff given to the coalition was directly prOportional to the number of points that the members of the coalition had remaining relative to the total number of points remaining. The last lO8 games played by each triad were in the pure truel condition. The type, number, and order of games that were played by each triad is reported in Table 2. A6 Table 2. Type, Number, and Order of Games Played by Each Triad Number of Games Played by Triads Type of Game Isz 35A 556 738 Pure Truel 360 360 360 360 Pass Option I80 l80 I80 l80 Non-Aggression I80 Mutual Defense I80 Coalition (SO/50) I80 Coalition (Parity) I80 Pure Truel IO8 IO8 IO8 l08 To reduce the probability that the members of the triad would be able to determine which player was which in a preceding game the labels and the number of points that each player could remove were counterbalanced for each game and the counterbalanced games were randomly distributed within 36 game sessions. Position effects were reduced by assigning the subjects randomly to one of the three player positions in the table divider for each set of 36 games. The labels on the communication terminals were counterbalanced so that no button position preference would bias the data. In addition, the labels on the scoreboard were randomly assigned each day. The counter- balancing and randomizing procedures were designed to reduce the probability that the members of a triad would be able to match a player with a playing position from one game to another as well as controlling for position effects and attack button preferences. Results and Discussion The data from the present experiment falls into two distinct categories; (I) data relevant to pure uelative conflict, and (2) data relevant to potential uelative conflict. Thus, the presentation and interpretation of the results for those two categories are treated separately. Following the initial presentation of the pure uelative conflict and potential uelative conflict data, the observed probability of attacking given an Opportunity to attack, the mean number of attacks per game, and the probability of survival is compared for all game types in all of the conditions. That data is examined to determine which, if any of the manipulations employed in the potential uelative conflict games resulted in a reduction in the level of conflict. To simplify the presentation of the data, the relationship be- tween players was considered to be such that A>»B>’C (see Table l). Player A's stronger Opponent was player B, and player 8 and C's stronger Opponent was player A. For consistency, in the all equal (6/6/6) game, the relationship between players was also defined to be A>-B>IC. Thus, even though player A and player C could each remove six points, player A is referred to as player B's stronger Opponent. Player A is also referred to as player C's stronger Opponent, and player 8 is referred to as player A's stronger Opponent. A Test of the Cole and Phillips Model Pure Truel Results. The model prOposed by Cole, et. al., is applicable only to the pure uelative conflict situation. Since there was a possibility that learning effects over trials might modify the behavior in the pure uelative conflict games, a 3x6xl3 analysis of variance with repeated measures on all three factors was computed on A7 A8 the observed probability of attacking the stronger Opponent for each of the three values of D(X), in each of the six game types, for the l3 thirty-six game sessions of the pure truel. Groups were the unit of analysis, and while no attempt was made to examine the between groups variance, it was partialed out of the within groups variance. Table 3 reports the mean probability of attacking the stronger Opponent and standard deviations for Player Position, Session Number, and Game Type. A summary of the analysis of variance is presented in Table A. The purpose of the analysis of variance was to determine if any learning effects were present over sessions in the truel. There was a significant effect for Game Type (F=l7l.059, p < .0005) and Player Position (F=IA.5ll, p < .0005) as well as significant interactions between Game Type and Session Number (F=I.6l3, p ==.OOA) and between Game Type and Player Position (F=l3.2lA, p < .0005). There was no significant effect for Session Number (F=.8I9, p z .630). Figure 3 and Figure A present the mean probability of attacking the stronger Opponent for Game Type by Session Number and for Game Type by Player Position respectively. It is obvious from Figure 3 that the interaction is a function of the variance within game type. The data presented in Figure 3 and the lack of any significant differences between the mean probability of attacking the stronger IOpponent within any game type as shown by a Scheffe's multiple comparison t-test (Scheffe', I953), suggests that there is no difference in the probability of attacking the stronger opponent as a function of session number. Figure A suggests that, for the most part, the game type by player position interaction is a function of the strategy choices of players A and B in the 7/6/5 and 8/6/A games and A9 0.. 00. ... 00. m0. 00. 00. 00. 00. 00.. m0. 00. 0.. ... 00. N0. 00. 00. m. ... 0.. .0. N0. 00. 00. 00. 00.. m0. 00. 00. mm. 00. 0.. .0. 00. N0. 00. N. 0.. 00. NN. .0. 00. 00. mo. 00. 00. 00. .0. 0m. 00. 0.. 00. 00. m0. m0. .. N.. 00. m.. N0. m0. mm. 00. 00.. 00. 00. 00. 00. 00. me. 00. m0. 0.. m0. 0. «N. 0.. 0.. 0A. 00. 00. 00. 00.. mo. .0. 00. 00. 00. 0.. 00. N0. N0. 00. 0 mm. 00. 0.. N0. 00. 00. 00. 00.. 00. 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NA. .0. 00. 0.. 00. 00. 00. 00. mm. 00. 00. ... 0m. 00. m0. 0.. 0m. 0 00. me. 00. 00. 0.. 00. 0.. 0m. N0. 00. .0. mm. 0.. 00. 00. 00. 00. 00. N 0.. .0. 0.. N0. 00. .0. m.. 00. 00. 00. 0.. Am. 0.. 00. 0.. 00. 0.. 00. 0 0.. N0. m.. .0. 0.. 00. 0.. 00. .0. .0. mo. 00. 0.. 00. 0.. 0m. 0.. 00. m 00. ... ... 00. 00. N0. N0. 00. N0. N0. 00. mm. ... m0. 0.. km. 0.. 00. 0 ... me. 00. ... N0. 00. m.. 00. 00. 00. 00. 00. 0.. 00. ... mm. ... 00. m 0.. .0. 00. 00. 00. ... m0. 00. 00. mm. 00. 00. 0.. 00. ... 00. 00. 00. N 0.. 00. m.. 00. 00. m0. 0.. N0. 0.. mm. 0.. 00. 0.. 00. 00. 00. e0. 00. . unpasz 00 m 00 m 00 m 00 m 00 m 00 m 00 m 00 m 00 m 00.0000 0 m m u m < co_u_mOm :\0\m m\0\m 0\w\m oa>h OEmw consaz co_mmOm vcm .OQ>F OEmo .co_u_mom co>m_m co» mco_um_>oo Ucmocmum ocm ucocooao cochLum ozu mc.xumuu< mo >u.__nmno.m cmoz .m o_nmk 50 Table A. Summary of Analysis of Variance on Attack Data Summarized in Table 3 Approximate Source SS df MS F Significance Level Between Groups (A) .A88 7 Within Groups 72.052 l86A Game Type (B) A6.262 5 9.252 l7l.059 <.0005 AB l.893 35 .05A Session Number (C) .l56 l2 .Ol3 .8l9 .630 AC 1.339 8A .015 Player Position (D) .320 2 .l6O lA.5ll <.0005 AD .l5A IA .Oll BC l.038 60 .0l7 l.6l3 .OOA ABC A.509 A20 .OlO BD I.96l l0 .l96 l3.2lA <.0005 ABD l.039 70 .OlA CD .386 2A .0l6 l.307 .l66 ACD 2.068 I68 .Ol2 BCD l.lOA l20 .009 .752 .97A ABCD l0.266 8A0 .Ol2 Total 72.990 l87l 5l _ m. I N mco_mmom .consac co_mmOm vcm uo>u OEmm co» .macu mesa Oz» c. Aucocooao cochLOm ozu mc_xumuum_a new oa>u OEmm to» .Oscu mesa Ozu :. Aucocoaqo Lomcocum ecu mc_xomuumvm com: :0). ~33. m\0\m 03$ m\0\m 0\0\0 _ AI . . _ 0 x Q IIIIIIIIIo ‘\$ 0 \c 4 q X IIIIIIAV u .O>m.m o Illlllfl m Lo>m_m . I. < Lere... I 0x4 .: o.:m.u 0. (Juauoddo JESUOJls sq: Sulxoellv)d 53 of players A and B and of players A and C in the lO/6/2 and ll/6/I games. A series of potential uelative conflict sessions (36 games per session) were introduced between the first ten sessions and the last three sessions of the pure truel. The data from the three pure truel sessions immediately preceding the potential uelative conflict sessions, and the three pure truel sessions immediately following the potential uelative conflict sessions were compared to determine how strategies in the pure truel might have been effected by the intervening potential uelative conflict sessions. Table 5 reports the mean probability of attacking the stronger opponent and standard deviations for Player Position, Pre and Post potential uelative conflict, and Game Type. A summary of a 2x3x6 analysis of variance with repeated measures on each factor which was computed on that data is reported in Table 6. As was the case in the analysis of the first l3 sessions of the pure truel, groups were the unit of analysis and the between groups variance was partialed out of the within groups variance. There was a significant main effect for Game Type (F=l53.AIA, p < .0005) and Player Position (F=lA.lA5, p < .0005) as well as a significant interaction between Game Type and Player Position (F=8.20A, p < .0005). Figure 5 presents the mean probability of attacking the stronger Opponent for Game Type and Player Position. As was the case over all thirteen sessions, the Game Type by Player Position interaction appears to be a function of the strategy choices of players A and B in the 7/6/5 and 8/6/A games and of players A and B and players A and C in the l0/6/2 and ll/6/l games. In addition, there appears to be an interaction between players 8 and C in the lO/6/2 5A mm.. 000. .m.. .00. mmo. 0mm. mm.. «mm. mmo. Mom. 000. 0mm. .\0\.. 0N0. 0mm. 0.0. 0mm. 0:0. mkm. moo. mmm. 000. mmm. N00. 00m. N\0\0. Nuo. .mm. 0m0. 000. umo. 0m0. 0.0. m00. 0M0. ..0. 000. 000. M\0\m mmo. .00. .mo. :00. 000. 0.0. N00. 000. N00. mm0. mmo. mm0. 0\0\0 000. .m0. .00. mmm. «mo. mwm. .00. mmm. mmo. 0N0. 000. 000. m\0\m 0... 0mm. .00. Nm:. 0... m.m. 0... ~00. 00.. RNO. N00. 00m. 0\0\0 Oo>k om M cm M 0m M mm N cm m cm M 0500 co.u.mOm 0 m < 0 m < co>m.¢ umOm 0.; uo..mc00 O>.um.o= .m.ucOuom 0000 cam mum 0cm .OQ>H OEmu .co.u.mOm co>m.m .00 mco_um.>mo venocmuw ocm .oack Oczm mg. C. “cocooao LO0c0cum ecu mc.xomuu< mo >u...0mno.m cmoz .m 0.0mh 55 Table 6. Summary of Analysis of Variance on Attack Data Summarized in Table 5 Approximate Source SS df MS Significance Level Between Groups (A) .l80A6 7 Within Groups .56346 280 Game Type (B) .A6360 5 I.A9272 153.AIA18 <.0005 AB .3A08A 35 .00973 Player Position (C) .l3693 2 .068A6 lA.lAA63 <.0005 AC .06789 IA .00A8A Pre-Post (D) .OOOOI l .OOOOI .OOIAO .969 AD .05025 7 .007l7 BC .A8323 l0 .0A832 8.2037A <.0005 ABC .Al283 70 .00589 BD .0298] 5 .00596 l.06A29 .397 ABD .l963O 35 .00560 CD .00580 2 .00290 .850AA .AA9 ACD .0A787 lA .003Al BCD .Ol837 IO .OOl83 .AlAO3 .935 ABCD .30973 70 .OOAA2 Total 9.7A392 287 56 .mOEmm 00...:oo O>.um.O: .m.u:OuO0 0000 new 0.0 0:0 0. 00.0.000 Lo>m.0 pcm O0>u 0500 .00 .0300 0030 050 c. Apcoco00o Lomcocum 0:0 mc.xomuumv0 :00: .0 0.30.0 .\0\.. N\0\o. M\0\m 0\0\w m\0\n 0\0\0 0. q a I a d I I m. \. .\. OIIIIIIIIIIII c Q x QIIIIQ 0 1.90.0.0 XIIIIIIIIX m um>m.0 x o o < Lo>m.0 . o (Juauoddo JBBUOJJS au: Bugxoennv)d 57 and ll/6/l games. There was no significant effect for the Pre and Post potential uelative conflict sessions. Moreover, since the F value was less than one for the Pre-Post effect (F=.OOlA), and the over sessions effect was considered minimal over all l3 sessions, the data for all l3 pure uelative conflict sessions were combined to test the model. The initial test of the model examined only the first trial data. The observed probability of each player attacking his stronger opponent on the first trial was considered to be equal to the ratio of the total number of times the stronger Opponent was attacked relative to the total number of attack Opportunities. Table 7 reports the number of times that players A, B, and C attacked their stronger opponent as well as the number of attack Opportunities and the probability of attacking the stronger Opponent for all six game types. To obtain the predictions of the model it was first necessary to calculate the number of reflective cycles associated with attack- ing the stronger Opponent in each of the three player positions (nA, n8, and nc). To simplify the calculation of the reflective cycles, a computer program was written by E. Alan Hartman which used a restricted range monte carlo procedure to predict the probabilities of attack on all trials for players A, B, and C for n = l to n = 6 at one tenth of a reflective cycle intervals. For the first trial only the types 7/6/5 through ll/6/l games were considered, since in the 6/6/6 game 'n' has no effect on the predicted probability of attack. That is, regardless of 'n', in the 6/6/6 game the predicted probability of players A, B and C attacking either of their opponents 58 Table 7. Predicted and Observed First Trial Attacks and P(Attack) on the Stronger Opponent* Attacks P(Attack) Game Type Player Predicted Observed Predicted Observed A 3I2 3A2 .50 .55 6/6/6 B 3I2 286 .50 .A6 C 3l2 297 .50 .A8 A A78 517 .77 .83 7/6/5 B A86 A86 .78 .78 C A7A A7A .76 .76 A 590 537 .87 .86 8/6/A B 559 5A7 .90 .88 C 53l 507 .85 .8I A 570 558 .9] .89 9/6/3 B 59l 578 p.95 .93 C 5A9 562 .88 .90 A 585 602 .9A .96 l0/6/2 B 608 6lO .97 .98 C 552 605 .88 .97 A 607 603 .97 .97 Il/6/l B 6l9 530 .99 .85 C 5A0 A95 .87 .79 *Note.--There were 62A opportunities to attack for each power position in each game type. 59 is .5. Thus, the 6/6/6 game was not included in the calculation of 'n'. Table 8 presents the Observed n's for each player position in each game type. A 3x5 analysis of variance on the observed n's revealed a significant effect for both Game Type (F=6.85, p < .05) and Player Position (F=7.ll, p < .05). A summary of that analysis of variance is presented in Table 9. A Duncan's multiple range test (Edwards, I960, p. I36) was computed on the 37$ for player position. Table l0 reports the results of that test which indicated that there was no significant difference between the h for players A and C. However, 3 for player B was significantly lower than 3 for players A or C (p < .05). Such a result supports Hypothesis l which prOposed that nB < ”A = nc. Support for Hypothesis l adds credibility to the assumption ‘hat as the disparity of the strengths of a player's attack alternatives increases, 'n' decreases. A Duncan's multiple range test reported in Table II, was computed on the 375 for each game type. The results of that test indicated that the h for the 7/6/5 game was significantly different from the Hus for the 9/6/3, l0/6/2, and ll/6/l games (p < .05). The F for the ll/6/l game was significantly different from E for each of the other game types. There was no significant difference between the 375 for the 8/6/A, 9/6/3, or l0/6/2 games. Except for the reversal of the l0/6/2 and 9/6/3 n's, the n's were ordered such that the assumption that there is an inverse linear relationship between game type and 'n' was supported. Since there was no significant difference be- tween n for the IO/6/2 and 9/6/3 games the exception was not considered to be such that that assumption should be rejected. Therefore, a 60 Table 8. Observed and Estimated n for Players A, B, and C Attacking Their Stronger Opponent in Game Types 7/6/5 through ll/6/l on Trial l Game Type ”A n3 nc Observed Predicted Observed Predicted Observed Predicted 7/6/5 2.l l.7 .9 l.9 l.9 l.9 8/6/A l.2 l.2 .5 .7 l.3 l.6 9/6/3 .6 .8 .2 .A l.A l.3 lO/6/2 .6 .3 .2 .2 l.8 I.O ll/6/l .O .O .0 .0 .0 .6 Table 9. Summary of Analysis of Variance on n for Players A, B, and C in Game Types 7/6/5 through ll/6/l Source SS df MS F Game Type (A) A.ll73 A l.0293 6.85* Player Position (B) 2.l373 2 l.0687 7.ll* AB l.2027 8 .ISOS Total 7.A573 IA P < .05 6l Table l0. Summary of Duncan's Multiple Range Test on Mean n's for Players A, B, and C Player B Player A Player C EPOFF:?F lgnI Icant Means .36 .90 l.28 Range .36 .5A .92 .5A .90 .38 .55 N0te.--Underlined means are not significantly different, a = .05. Table II. Summary of Duncan's Multiple Range Test on Mean n's for Game Types 7/6/5 through ll/6/l II/6/l 9/6/3 10/6/2 8/6/A 7/6/5 :horfiét IgnI Icant Means .OO .73 .87 I.OO l.63 Range .00 .73 .87 l.00 l.63 .72 .73 .IA .27 .90 .75 .87 .I3 .76 .76 l.OO .63 .77 Note.--Underlined means are not significantly different, a = .05. 62 linear regression procedure was used to determine the best fit linear approximation to the observed n's. The best fit linear approximation Figure 6 presents a graphic was then used to estimate fl RB, and n A’ c' representation of the observed n's and the linear approximation. Table 8 reports those data in tabular form. The predicted first trial probabilities of attacking the stronger opponent which correspond to the estimated n's for players A, B, and C in all six game types are presented in Figure 7 and Table 7. Figure 7 also reports the observed probabilities of players A, B, and C attack- ing their stronger Opponent for all six game types. It is obvious from an examination of Figure 7 that the model does not provide a perfect fit. However, it is equally obvious that, except for the ll/6/l game for player 8 and the lO/6/2 and ll/6/l games for player C, it offers a reasonable approximation of the observed attack probabilities on the first trial. The poor fit can be partially accounted for by a rather surprising phenomenon which occurred in the ll/6/l games. For players B and C the ll/6/l game was very frustrating. They were forced to participate in a competitive situation in which their chance of winning was zero provided that player A chose to win. As a result, in many instances, players B and C chose to attack their weaker Opponent; thus, ending the game one trial earlier than it would have ended had they followed the predictions of the model. In essense, players B and C formed implicit mutual aggression alliances to shorten the amount of time Spent in the ll/6/l game. Such reasoning is reflected in the rapid drOp between the lO/6/2 and ll/6/l games in the number of times that the stronger opponent was attacked. Player A, on the other hand, does not redefine the payoff. 63 ... .0..hv 0003.OX0 m. 00>. 0500 .\0\.. 0;. c053 0 0:0 0 m.0>m.0 .0. 0:0 .\0\.. £030.50 m\0\m 000>p 0500 c. 0 0cm .0 .< m.0>0.0 .0. c o. co.ume.xo.000 .00:.. 0.. 0000 0:0 0:0 .0. m0.o>o 0>.000..0. .0 .0053: 0:0 .0 0.30.0 0 . m 0 . 0 0 0 0 0 0 0 0 . 0 . 0 . m 0 0 0 .. m «00on dlxxom m 0 m d dwwd 0 0 0 1I\\O dl\\OL{\ QC L mC .1 (C I IIIIII 0003.88 .\0\.. II.IIIIII 0003.0c. .\0\.. co..mE.xo.00m .00:.. 0.. .000 I CC seloAg aAlloaljag 6A .A. .0..Hv 000>u 0500 x.m ..0 .00 00000000 .0000.00 ..050 0c.xomuum 0 0:0 .0 .< m.0>m.0 .0 >0...000O.0 000 .0 0.30.0 . N m 0 m 0 . N m 0 m 0 . N m 0 m 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .. 0. m 0 m 0 .. 0. m 0 0 0 .. 0. m 0 n 0 0 . q u H . q I~ ~ 4 ~ 4 0 d u a J . / / +IIII| + 0050000 0 O U®uo__u®.n_ l. + o .0 00.0ueuu< 0.0 .< 00.0u0000 0.0 .0 00..uc..< <00 + +\ .. . . + \ \.\ .... +IA+ 0.. 65 For player A the IOO points payoff remained salient and he continued to approximate the behavior predicted by the model. A graphic representation of the linear approximation to 'n' across game types was again used to estimate nB and nc; however, the ll/6/l game was not included. Figure 6 reports the estimated nB and nc across game types 7/6/5 through lO/6/2. Table l2 reports the estimated n for players B and C, the observed and predicted number of attacks on the stronger opponent, and the probability of attacking the stronger opponent in the 6/6/6 through lO/6/2 games. Figure 8 presents the observed and predicted probability of players 8 and C attacking their stronger opponent given nB and nC estimated excluding the Il/6/l game. A product moment correlation comparing the predicted and Observed probability of attacking the stronger Opponent for each of the three player positions indicated that the model does offer a reasonable approximation of the observed behavior (rA = .99; r8 = l.OO; and rC = .99). However, chi-squares computed on the same data revealed a significant difference between the predicted and observed number of attacks when the attacks on both the stronger and weaker opponent were considered for player A (X2 = 35.08, df = II, p < .Ol) and player c (x2 = I9.2i, df 9, p < .05). A chi-square computed on the same data for player B (X2 = ll.55, df = 9, .20 < p < .30) indicated that the model offers a reasonable account of player B's behavior. The ll/6/l game type was excluded when considering the fit of the model for players B and C. Even though the data indicated that the Cole and Phillips model offered a reasonably good fit, to the first trial data, by 66 Table l2. Estimated n, Observed and Predicted Attacks on the Strong Opponent, and the P(Attacking the Strong Opponent) for Players B and C in the 6/6/6 through l0/6/2 Game Types Trial l)* Attacks P(Attack) Game Type Player n Predicted Observed Predicted Observed we 5 31% 333 :23 :22 ms 5 I :2 2Z3 I32 :33 2?? W. E I :2 ii? 333 233 23? 9/6/3 E Iii 535 523 :3: :38 low/2 E I :I 23% 23.2 232 233 *Note.--There were 62A Opportunities to attack for each player position in each game type. 67 ... .0.... N\0\0. 0000.0. 0\0\0 .00.. 0000 .0. “00:0000 .0000.00 ..000 0:..00000 0 000 m m.0>0.0 0o >0...0000.0 000 .0 0.30.0 N m 0 m 0 N m 0 m 0 0 0 0 0 0 0 0 0 0 0 0. 0 w m 0 0. m m m 0 0. 1 . . . . 1 . . . / + +v0>.0m..0 / 0 00000.00; 0 .. .... m. I 0. .< 0e..ue..< 0.0 .< 00.xu0000 0.0 I. 0. IT + I e. \. .xkawxxxxx .wnu““r .. 0 IT 0.. 68 statistical standards it was rejected. A chi-square that is larger than the degrees of freedom is reason enough to reject a model. Moreover, chi-squares that are large enough to reach significance levels of .05 and .Ol are obvious reasons to reject a model. However, the product moment correlations between the predicted and observed first trial data indicate that the model should not be discarded even though it is rejected. That is, even though the model was statistically rejected there is evidence that it accounts for much of the first trial behavior in the truel. In all of the game types, on all trials following the first trial, R(X) changed as a function of who had attacked whom on the preceding trial. Therefore, on all trials following the first trial, R(A), R(B), and R(C) were assigned values equal to the average number of points that players A, B, and C had remaining at the beginning of each trial. The average number of points was computed by counting the number of points controlled by each player position in each of the total games remaining on a given trial for all groups, multiplying by the probability of each of the players controlling that many points, and summing the resulting values. Table I3 lists the computed number of reflective cycles for players A, B, and C on the second, third, and fourth trials in the 6/6/6 and 7/6/5 games and on the second and third trials of the 8/6/A through ll/6/l games. Only the second and third trials are reported in the 8/6/A through ll/6/l games because less than IO of the 62A games played in each of those game types lasted more than three trials. Since, with the exception of the 6/6/6 game, 'n' seemed to be relatively stable across all trials following the first trial, 69 Table I3. Computed n and Estimated 8 for Players A, B, and C on Trials Following Trial l in Game Types 6/6/6 through ll/6/l* n Game Type Player Trial 2 Trial 3 TrialwA A 0.0 0.0 0.0 0.0 6/6/6 B 0.0 1.9 0.0 0.6 C l.8 2.A O.A l.5 A 0.0 0.0 0.0 0.0 7/6/5 B 0.0 0.0 0.0 0.0 C 0.0 0.0 0.0 0.0 A 0.0 0.0 0.0 8/6/A B 0.0 0.0 0.0 C 0.0 0.0 0.0 A 0.0 0.0 0.0 9/6/3 B 0.0 0.0 0.0 C 0.5 0.0 0.3 A 0.6 0.0 0.3 l0/6/2 B 0.3 0.0 0.2 C l.7 2.l l.9 A 0.0 0.0 0.0 ll/6/l B 0.0 0.0 0.0 C 0.0 0.0 0.0 *Note.--Only trials in which N > l0 were reported. 70 n was estimated by taking the average nA, nB, and nc for all trials following the first trial in each game type. These estimated n's are reported in Table I3. Table IA presents the predicted and observed number of times that the stronger Opponent was attacked and the associated probabilities of attacking the stronger Opponent for players A, B, and C in each game type on all trials following trial one. Product moment correlations computed on the predicted and observed attacks on the stronger Opponent indicated that player C's behavior was approximated closely by the model on both Trial 2 and Trial 3 over all game types (Trial 2, rC = 1.00; Trial 3, rc = .99). The correlation coefficients for = .92); player A and B were low (Trial 2, r = .92; r = .88; Trial 3, r A 8 thus, for players A and B it was obvious that the mOdeI would be A rejected by statistical criterion. Therefore, no further analyses were run on the data for players A or B. Chi-squares computed on the attack data for player C indicated that the model Offered an acceptable fit on Trial 2 (X2 = 8.79, df = II) but that the model was rejected on Trial 3 (X2 = l8.29, df = II). Figures 9 and lo present a graphic representation of the attack data on Trials 2 and 3 reSpectively. Chi-squares computed on the attack data from Trial A in the 6/6/6 and 7/6/5 games indicated that player A's behavior was predicted by the model (X2 = l.69, df = 3). On the other hand, both player B's and player C's behavior rejected the predictions of the model (x: = 250.75, df = 3; x: = IOA.AI, df = 3). To further test the fit of the model correlation coefficients and chi-squares were calculated using the predicted and Observed attack 7l mu.e ..u.0 ..u.0 .0.:o.umx mm.m.flwx mm.u0. mm.muwx oo..u0. 00.00Numx N0.u0. 00.n0. 00..-«x H0 .0... .0.u<. um .0... N0.u<. H N .0... .v0u.O00. 0.03 0. 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N«0 :1. 4 . ., 4 00 _ 14 _ _ _ . _ o 1 IT l + 003.0030 // . o 00.0.00.0 / + .. .. \. \ .< 00.xo00.< 0.0 . .< 00.xu0..< 0.. .0 0:.x00..< <.0 7h data over trials within each player position in each game type. Table l5 reports the resulting correlation coefficients and chi-squares. In the 6/6/6 game both player B and C's attack behavior over trials was predicted by the model (XE = 6.67, df=7; x: = 2.0l, df=7), and player A's predicted attack behavior over trials was a reasonable approxima- tion of the observed behavior (Xi = 8.95, df=7, .20 < p < .30). With the exception of player C in the 8/6/4 game type (X2 = 7.h5, df=5, .lO < p < .20), all of the predicted behavior represented by over trials attack data was significantly different from the observed data at, less than the .05 level. On the other hand, the correlation coefficients were all high ranging from .97 to l.00 for all player positions in all game types. Table 16 reports the observed and predicted frequencies of survival for players A, B, and C as well as the observed and predicted frequency of no player surviving in the pure truel games. Figure ll is a graphic representation of those data transformed into the probabilities of survival and the probability of no player surviving. Product moment correlations computed on the predicted and observed frequencies of survival indicated that the model was able to make a reasonable prediction of player A's probability of survival (rA = l.00). However, the correlation between the predicted and observed frequency of survival was low for player B (rB = .82) and player C (rC = .67), and the correlation between the predicted and observed frequency of no player surviving was even lower (rNS = .57). Chi-squares computed on the data for player A and player B rejected the hypothesis that there was no difference between the predicted and observed frequency of 2 B survival (X2 = 59.88, df=ll, p < .0]; X A = l23.72, df=ll, p < .01). 75 Table l5. Correlation Coefficients and Chi-Squares Comparing the Attack Data Across Trials, Within Game Types and Player Positions Game Type Player r X2 df A 1.00 8.95 7 6/6/6 B .99 6.67 7 C .99 2.01 7 A .98 27.66 7 7/6/5 B .99 3A3.23 7 c 1.00 140.33, 7 A 1.00 113.80 ' 5 8/6/h B .98 121.53 5 C l 00 7 45 5 A .97 20l.05 5 9/6/3 B .98 780.99 5 C .99 ll.93 5 A l.00 29.26 5 l0/6/2 B l.00 l32.26 5 C .99 9.8A 5 A l.00 3l.23 5 ll/6/l B l.00 —-—-- 5 C l.00 28.97 5 76 Table 16. Observed and Predicted Frequencies of Survival and of No Player Surviving Game TYPe 6/6/6 7/6/5 8/6/h 9/6/3 10/6/2 11/6/1 Player A Predicted 170.72 130.16 121.68 99.80 100.83 590.67 Observed 137.28 90.22 107.95 79.87 56.78 590.93 2 XA=59.88, df=ll Player B Predicted 121.06 151.63 69.89 93.60 9.98 1.25 Observed 139.9l 117.31 121.06 hh.93 8.7% 8.ll x§=123.72, df=ll Player C Predicted 234.00 33l.3“ 321.98 “l6.83 62.00 27.06 Observed lhl.02 lhh.77 164.11 69.89 31.82 l6.22 No Survivor Predicted 90.22 6.20 111.07 10.35 007.01 .62 Observed 212.78 267.70 230.88 029.31 526.03 8.74 l .0 O\O\O‘ UTO‘Nb 4-‘0‘03— 77 P(Player C Surviving) 1 9 6 3 P(Player A Surviving) r'\ - \+ I l J Figure 11. 1 _J 6 7 8 9 10 II 6 6 6 6 6 6 6 5 A 3 2 1 pure truel. l. P(No Survivor) wO‘kOr. J 10 l 6 2 u—nmu—d P(Player B Surviving) + Predicted. Observed-f .41” X. / 1 7 6 6 5 Observed and predicted P(survival) and P(no survivod for the 78 Since the predicted and observed probability of player C surviving and the predicted and observed probability of no player surviving were obviously more diSparate than for player A or B, no chi-squares were computed on those data. It was obvious that the model did not meet a statistical criterion for goodness of fit; thus, the model was rejected with respect to probability of survival. Discussion. it is apparent that the model as prOposed by Cole and Phillips must be rejected. It is equally apparent; however, that it should not be discarded. What is indicated, is a refinement or revision of some of the basic assumptions of the model. For example, consider the assumption that the probability of attack is independent over trials. While such an assumption may prove valid, it appears that an acceptable alternative approach would be to assume dependence across trials. The fact that a player has been attacked previously might lower the probability that he would be attacked on the next trial. Of course, such a compassion effect would also be some function of the relative strengths of the participants. it would seem that the stronger an individual is relative to the attacker as well as to the attacker's alternative attack choice, the longer it would take for the compassion to build up to the level necessary to overcome the threat. Such a revision of the assumption of independence over trials would offer one explanation of the consiStent over predictions of the probability of attacking the stronger Opponent on Trials 2 and 3 as indicated in Figures 9 and 10. The data from player B questions the feasibility of the assump- tion that compassion might effect attack strategies as a function of previous attacks and the relative strength of attack alternatives. 79 if the compassion assumption were valid, it would seem that player B would not be effected by compassion before either player A or player C due to the greater disparity of his attack alternatives. That is, the threat of A to B relative to the threat of C to B is much stronger than the threat of B to C. Thus, it should take more moves for the effects of compassion to overcome the threat of A to B than the threat of A to C. In fact; however, based on the results of the present study, if the compassion assumption is correct, it must be the case that the greater the disparity of the attack alternatives, the faster the compassion builds up to a level that overcomes the threat. Player B must reach the level of compassion for player A that will overcome A's threat before the same effect is evident with respect to player C's com- passion for player A and player A's compassion for player B. Since such an assumption seem unreasonable, the compassion assumption is questionable if it is intended to account for all of the discrepencies between the predicted and observed attack data. The observed attacks of player B suggest that the assumption of independence between trials made by Cole and Phillips (1969) and Cole, Phillips, and Hartman (in preparation) may be valid. The over estima- tion of the attacks on the stronger Opponent might be a function of the difficulty in determining the threat of each of the other players when more than one resource dimension is varied. Such an assumption is sup- ported by the fact that the model fits well in the 6/6/6 game over trials for all players as well as in the first trial over all game types for all players (excluding the ll/6/l game type for players B and C). On the first trial of all game types only D(X) is varied and over trials in the 6/6/6 game only R(X) is varied. Thus, the participants 80 have to consider only one resource dimension. Over trials in the games other than the 6/6/6 game the participants must consider two resource dimensions. Given the nature of the manipulation of D(A) and D(C) relative to D(B) it is reasonable to assume that players B and A would have the most difficulty in determining which player is most threatening. After the first trial R(A) is usually less than R(C) while D(A) remains greater than D(C). Thus, player B is faced with a somewhat ambiguous situation which might result in a closer approximation of random behavior than would be predicted by the model. The attack data for player A can be interpreted similarly. Player C, on the other hand, is not faced with the same ambiguity after trial one that players A and B were faced with. In most cases player C has not been attacked and R(C) has remained at 20 for the second trial. Moreover, in the game types examined by the present experiment, both players A and B have usually been attacked such that R(A) and R(B) are approximately equal. The disparity of D(A) and D(B) remains the most salient resource dimension for player C when he determines relative threats. Thus, player C's behavior approximates the predictions of the model better on trial two than does either player A's or player B's. After Trial 2 has been completed; however, the relative importance of the resource dimensions becomes more ambiguous to all participants. In many cases R(X) is such that any participant can eliminate any other participant and the resource dimensions essentially become meaningless. Thus, on Trial 3 the disparity between the predicted and observed attack data increases. Although both suggestions offered above or some combination of those suggestions might account for much of the disparity between 81 the observed and predicted attack data, they are not the only possible alternatives. One equally acceptable alternative is to revise the weight given to R(X) when determining the threats. If R(X) is given more weight when determining the threats, the predicted probabilities of attacking the stronger opponent would be lowered on trials following trial one. In fact, it would be more acceptable to say that the strength associated with D(X) would be reduced as the strength asso- ciated with R(X) was increased. As a result the strength of the attack alternatives would be revised. Since, on the second trial, R(C) would be the largest value of R(X), both player A and player B would tend to make more attacks on player C than is predicted by the present model. Moreover, player C would be the least effected by the re- weighting of R(X) since the size of R(A) and R(B) relative to each other is not effected greatly by attacks on trial one. Thus, by reweighting R(X) we would lower the second trial predicted attacks on player A and B by each other and cause little effect on the pre- dictions concerning player C's behavior. The predicted effect over trials would roughly SUpport the observed Trial 3 data reported in Figure 10. In addition, any revision of the weighting of R(X) would have no effect on the trial one data and little effect on the data over trials in the all equal game, since the relative disparity of R(A), R(B) and R(C) tends to remain constant over trials. If one considers the effects of such a reweighting of R(X) on the predicted probability of survival, it is apparent that, an increase in the predicted propensity to attack player C after the first trial would decrease the predicted probability of player C surviving. As a result the observed and predicted frequencies of 82 survival for player C would be less diSparate. However, it is not apparent that the gross overprediction of player C surviving would be corrected. Moreover, it is difficult to visualize how the reweighting of R(X) would correct for the underprediction of no player surviving. One possible eXplanation for both the overprediction con- cerning player C's survival and the underprediction concerning no player surviving may be a function of an equalization of strengths as the game nears the end. For example, consider a game in which on the last trial, D(X) for all players is greater than R(X) for all players. In essense the players have become equal in strength and must choose an attack based on other cues. Since all of the players are better off if no player wins than if one of the other players wins, it is sensible to assume that each of the players in such a situation will attempt to choose that strategy which maximizes the chance of no player winning given that he does not win. Such a strategy might account for the observed propensity for no player to win below the dictator region. Unfortunately, the data from the present study does not lend itself to an examination of such a hypothesis; thus, further research is indicated. Potential Uelative Conflict Pass Option Results. Hypothesis 2, that the prOpensity to pass increases as the diSparity of relative strengths decreases was the only hypothesis relevant to the pass Option games. To test that hypothesis, a probability of passing score was calculated for each power position in each game type for each of the eight eXperimental groups. The probability of passing score was considered to be the 83 ratio of the total number of passes for each player position in each game type relative to the total opportunities to pass. Table 17 reports the resulting scores. A 3x6 analysis of variance with repeated measures on both factors was computed on the data in Table 17. Table 18 reports a summary of that analysis. Since groups were the unit of analysis, the between groups effect was not examined; however, the between groups variance was partialed out of the within groups analysis. The results of that analysis revealed a significant effect for Game Type (F=h.57, p < .01) and a significant interaction between Game Type and player position (F=h.67, p < .01). Scheffe's multiple comparison t-tests of the means relevant to the interaction suggested that the behavior in the 11/6/1 game was responsible for the significant interaction. In the ll/6/l game, the mean probability of passing for player A was significantly different from the mean probability of passing for player C (tAc= 7.103, t'=5.089, a = .01), and the mean probability of passing for player B (tAB=4.6h3, t'=4.039, a = .05). There were no other signifi- cant differences between players within any of the six game types. To further test Hypothesis 2, a revised analysis of variance identical to the previous analysis except for the exclusion of the ll/6/l data was computed on the data in Table 17. A summary of the 3x5 analysis of variance with repeated measures on both factors is reported in Table 19. The results of the analysis of variance revealed a significant effect for Game Type (F=8.33, p1< .001) and no other significant effects. The significant effect for game type did not necessarily support 8h 0m. .N. mo. mo. «o. co. :N. No. .o. mm. .o. .o. ... :o. oo. :9. mo. .0. m no. 00. oo. 00. oo. oo. N.. no. m.. m.. mo. m.. w.. ... .N. om. mm. mm. m oo. mo. oo. oo. oo. oo. mo. oo. mo. .0. oo. mo. .0. No. oo. :0. mo. mo. mmw mo. mo. oo. oo. oo. oo. .o. oo. oo. .o. 00. mo. «0. no. «O. m.. mm. m.. mm no. 00. 00. No. oo. 00. no. mo. No. mo. mo. mo. mo. no. m.. no. .3. mo. .NW 5.. No. 00. oo. oo. oo. .o. .o. .0. mo. mo. No. :0. mo. mo. 0.. mo. mo. mum NM. RN. mo. no. mo. mo. .N. NN. mm. mm. NN. Na. mm. mm. mm. :m. om. ~:. ~ am. m:. No. No. mo. mo. 0.. :0. wo. we. no. N.. N.. m.. no. mm. mm. 5N. . u m < u m < u m < u m < u m < u m < cOwwMMwM .\o\.. ~\o\o. mxmxm :mew m\o\N mxoxo 00>. 050a 0a>h 0500 0:0 cO.~.wO¢ .0>0.m 0.00m m:.mmmm mo >0...20nO.¢ .m. 0.30h 85 Table 18. Summary of Analysis of Variance on Data in Table 17 (11/6/1 Included) Source SS df MS F Game Type .32 5 .064 4.57* Game Type x Between 55 .48 35 .014 D(X) .06 2 .030 3.33 D(X) x Between 55 .13 14 .009 Game Type x D(X) .14 10 .014 4.67* Game Type x D(X) x .20 70 .003 Between 55 Total 1.33 136 *p < .01 Table 19. Summary of Analysis of Variance on Data in Table 17 (ll/6/1 Excluded) Source SS df MS F Game Type .30 a .075 8.33* Game Type x Between 55 .25 28 .009 D(X) .02 2 .010 2.00 D(X) x Between 55 .07 14 .005 Game Type x D(X) .02 8 .003 1.50 Game Type x D(X) x .09 56 .002 Between 55 Total .75 112 *p < .001 86 Hypothesis 2; therefore, a Duncans Multiple Range Test with a signifi- cance level of a = .01 was computed on the means of the probability of passing scores across player positions within the 6/6/6 through 10/6/2 games. Table 20 reports a summary of that test. The results of the Duncans Multiple Range Test indicated support for Hypothesis 2. There was a significant difference between the mean probability of passing in the 6/6/6 and the 10/6/2 games; however, the mean probability of passing was not significantly different between the 6/6/6 through 9/6/3 games or between the 7/6/5 through lO/6/2 games. For all five game types the mean probabilities of passing were ordered such that the probability of passing increased as the diSparity of relative strengths decreased. Alliance Game Results. To test Hypotheses 3, 4, 8, and 9, two sets of data were examined; (1) the number of times that the stronger Opponent was contacted in the initial contact period (see Table 21), and (2) the alliances resulting from reciprocal contacts in the initial contact period (see Table 22). Only data obtained in the initial contact period were examined because it was assumed that the data reflected preferences for alliance partners which might be modified on subsequent trials. One-tailed Z-tests were computed on the contact data for each game type within each alliance condition reported in Table 21. To permit the use of the Z-test, the prob- ability of contacting either Opponent was assumed to be .5. Hypothesis 3 predicted that, in the non-aggression alliance games, the stronger of the other two participants would be the preferred alliance partner in the 7/6/5, 8/6/4, and 9/6/3 games. In the 7/6/5 and 9/6/3 non-aggression alliance games, Hypothesis 3 87 Table 20. Summary of Duncan's Multiple Range Test on Data in Table 17 (ll/6/l Excluded) Game Types lO/6/2 9/6/3 8/6/4 7/6/5 6/6/6 Shortest Significant Means .011 .077 .097 .100 .170 Range .014 .063 .083 .086 .156 .132 .077 .020 .023 .093 .138 .097 .003 .073 .143 .100 .070 .148 Note.--Underlined means are not significantly different, a = .01. 88 Table 21. Contacts in the Initial Contact Period in the 7/6/5, 8/6/4, and 9/6/3 Alliance Games Game Type 7/6/5 8/6/4 9/6/3 Combined Contact Choice Strong Weak Strong Weak Strong Weak Strong Weak Non-Aggression 99 72 94 80 103 71 296 223 Z-Test for Random Preference of 1.99* .99 2.35* 3.16** Alliance Partner Mutual Defense 28 78 47 S7 25 75 100 210 Z-Test for Random Preference of 4.71*** .88 4.90*** 6.19*** Alliance Partner Coalition Parity 22 141 20 145 22 144 64 430 Z-Test for Random Preference of 9.24*** 9.65*** 9.39*** l6.l4*** Alliance Partner Coalition 50/50 74 105 84 94 81 98 239 297 Z-Test for Random Preference of 2.32* .67 1.20 2.46* Alliance Partner ***p < .001 **p < .01 *p < .05 89 Table 22. Alliances Resulting from Initial Contacts in the 7/6/5, 8/6/4, and 9/6/3 Alliance Games Game Type 7/6/5 8/6/4 9/6/3 Combined Alliance Type AB AC BC AB AC BC AB AC BC AB AC BC Non-Aggression 27 IO 8 23 20 15 27 24 8 77 54 31 Q-Test for Random 1 10.59*** 1,69 10.6100 19.59*** Alliance Formation Mutual Defense 3 3 10 6 7 4 1 1 5 10 ll 19 Q-Test for Random 6.13* 82 “.57 3 65 Alliance Formation ' ° Coalition Parity 1 l 53 0 l 48 2 l 46 3 3 147 Q-Test for Random Not Calculated Alliance Formation Coalition 50/50 16 9 29 17 9 22 14 10 24 42 28 75 Q'Test for Random 11.44** 5.37 6.50* 24.1 *** Alliance Formation ***p < .00] **p < .01 *p < .05 INote.--df = 2 for all Q-tests. 90 was supported-~the stronger Opponent was contacted significantly more often than the weaker opponent (Z=1.99, p < .05 and Z=2.35, p < .05 respectively); however, it was not supported in the 8/6/4 game (25099). There was a significant propensity to contact the stronger Opponent for the combined 7/6/5, 8/6/4, and 9/6/3 data (Z=3.16, p < .01). To further test Hypothesis 3, three separate Q-tests (McNemar, 1957, p. 232), one each on the 7/6/5, 8/6/4, and 9/6/3 game types, were computed on the non-aggression games data to test the hypoth- esis that the number of AB, AC and BC alliances resulting from initial contacts was not different from zero. That hypothesis was rejected in the 7/6/5 (A=l4.59, df=2, p < .001) and 9/6/3 (Q=IO.61, df=2, p < .01) games; however, it was not rejected in the 8/6/4 game (Q=l.69, df=2). The rejection of the hypothesis indicated support for Hypothesis 3. Thus, Hypothesis 3 was supported by both the initial contact and initial alliance data in the 7/6/5 and 9/6/3 game. Hypothesis 3 was not supported in the 8/6/4 game. A Q-test on the combined 7/6/5, 8/6/4, and 9/6/3 initial alliance data SUpported Hypothesis 3 (Q=19.59, df=2, p < .001). Hypothesis 4 predicted that in the mutual defense games the weaker of the other two participants would be the preferred alliance partner in the 7/6/5, 8/6/4, and 9/6/3 games. The initial contact data reported in Table 21 supported Hypothesis 4 in the 7/6/5 and 9/6/3 games (Z=4.7l, p < .001 and Z=4,90, p < .001 respectively). Hypothesis 4 was not supported in the 8/6/4 game (Z=.88). The combined 7/6/5, 8/6/4 and 9/6/3 initial contact data SUpported HYPOth651S 4 (Z=6.l9, p < ~001). The alliances resulting from 91 initial contacts reported in Table 22 supported Hypothesis 4 in the 7/6/5 game (Q=6.13, df=2, p < .05), but it did not support Hypothesis 4 in the 8/6/4 or 9/6/3 games (Q=.82, df=2 and Q=4.57, df=2 reSpectively). Hypothesis 4 was not supported by the combined 7/6/5, 8/6/4 and 9/6/3 initial alliance data (Q=3.65, df=2). Thus, Hypothesis 4 was supported by both the initial contact and initial alliance data in the 7/6/5 game, was only partially supported in the 9/6/3 game, and was not supported in the 8/6/4 game. Hypothesis 8 predicted that a prOpensity to form weak coalitions would be manifest in the coalition (parity) games. The initial con- tact data reported in Table 21 supported Hypothesis 8 in the 7/6/5, 8/6/4, and 9/6/3 game types (Z=9.24, Z=9.65, and Z=9.39 respectively, p < .001). Further support for Hypothesis 8 is indicated by the combined initial contact data (Z=16.l4, p < .001). The alliances resulting from initial contacts reported in Table 22 were such that statistical analyses was not necessary. In the 7/6/5 game, 53 of 55 alliances were weak; in the 8/6/4 game, 48 of 49 alliances were weak; and in the 9/6/3 game 46 of 49 alliances were weak. For the combined initial alliance data, 147 of 153 alliances were weak. It was obvious that a prOpensity to form weak (BC) alliances was manifest in all three game types, and that there was strong support for Hypothesis 8 by both the initial contact and initial alliance data. Hypothesis 9 predicted that a random formation of coalitions would be manifest in the coalition (SO/50) games. A random preference for alliance partners was manifest in the 8/6/4 and 9/6/3 games as reported in Table 21. Moreover, in the 8/6/4 game a random propensity to form alliances was manifest as reported in Table 22. Hypothesis 9 92 was not supported; however, by the preference for alliance partners manifest in the 7/6/5 game (Z=2.32, p < .01) or the propensity to form alliances in the 7/6/5 and 9/6/3 games (Q=1l.44, df=2, p < .01 and 06.50, df=2, p < .05 reSpectively). Moreover, both the initial contact data and the initial alliance data indicated that there was a non-random preference for alliances in the coalition 50/50 game (Z=2.46, p < .05, and Q=24.IO, df=2, p < .001 for the initial contact data and initial alliance data respectively). Thus, Hypothesis 9 was only partially supported by the data. Hypothesis 5, 6, and 7 were concerned only with the mutual defense and non-aggression games at the veto point and in the dictator region--the lO/6/2 and 11/6/1 games. Table 23 reports the initial contact data for each player position in the lO/6/2 and 11/6/1 mutual defense and non-aggression games. The AB, AC, and BC alliances resulting from initial contacts in the lO/6/2 and 11/6/1 games are reported in Table 24. Hypothesis 5 predicted that the strongest player would be the two weaker players' preferred alliance partner in the 10/6/2 and ll/6/l games in both the mutual defense and non-aggression alliance games. The initial contact data from the mutual defense games not only failed to support Hypothesis 5, it indicated a significant propensity for the weaker player to be the preferred alliance partner (Z=6.67, p < .001 and Z=6.62, p < .001 for players B and C respectively in the 10/6/2 game and Z=3.73, p < .01 and Z=4.27, p < .01 for players B and C respectively in the 11/6/1 game). On the other hand, Hypothesis 5 was supported by the initial contact data in the non-aggression games (Z=7.36, p < .001 and Z=5.73. p < .001 «NN.: «MN.m on N .m N «mN.m «om.m O. m mm o. mm No.. No.0 om N ««mN.m N Nm «0Nm.m Nm N «0mm.N . mm 00.. mN m. m.. .m NN .o. v a« .oo. v a«« .0:u.0: 00:0...< .O 00:0.0w0cm 500:0x co. .005-N 00:0m0o .0303: .0:u.0: 0o:0...< .O 00:0.000L: 500:0: .Om umohnN :O.mmocmm<1:oz x00: mco:um x003 mco.um x003 m:O.um x003 m:O:um x003 m:O:um x003 acceuw 0u.o:u 0000:0u u m < u 0 < 00.0.00. .0.0.0 .NON.. NNmNo. 00.. 020a 00500 :o.mm0.mm<1:02 0:0 00:0000 .0203: .\m\.. 0:0 N\o\o. 0:0 :. :O.u.mo: .0>0.¢ :00m :0» muomu:0u .0.u.:_ .MN 0.005 94 Table 24. The AB, AC, and BC Alliances Resulting from Initial Contacts in the lO/6/2 and 11/6/1 Mutual Defense and Non-Aggression Games Game Type 10/6/2 11/6/1 Alliance Type AB AC BC AB AC BC ngfession 29 26 0 I O ' "”tua' 2 1 02 o 1 20 Defense 95 for players B anc C respectively in the 10/6/2 game and Z=3.90, p < .01 and Z=3.75, p < .01 for players 8 and C respectively in the 11/6/1 game). Hypothesis 6, that at the veto point the strongest player prefers to form an alliance with the weakest player in the mutual defense games and with the medium strength player in the non-aggression games was not supported by the initial contact data. One-tailed Z-tests computed on the initial contact data in both the non-aggression and mutual defense games indicated that the behavior of the strongest player was random (Z=.13 and Z=l.06 respectively). Hypothesis 7 predicted that in the mutual defense and non- aggression games within the dictator region, the strongest player would choose not to form an alliance, resulting in fewer alliances being formed in the 11/6/1 game than in any of the other games. Hypothesis 12 made a similar prediction for the coalition (parity) and coalition (SO/50) games. Table 25 presents the number of contact attempts made by player A in all four of the alliance conditions for game types 7/6/5 through 11/6/1. A 4x5 analysis of variance with repeated measures on one factor was computed on that data. Table 26 reports a summary of that analysis. A significant main effect was indicated for Alliance Type (F=51.57, p < .01), Game Type (F=529.8l, p < .001), and the Game Type by Alliance Type interaction (F=28.23, p < .001). Since Hypotheses 7 and 12 are not concerned with effects across alliance types or effects resulting from an interaction between alliance types and game types a Scheffe's multiple comparison t-test was computed which compared the mean prOpensity for the strongest player to make a contact between game types within each alliance condition. The results of that multiple Table 25. Number of Contacts Made by the Strongest Player 96 Alliance Game Type Type 7/6/5 8/6/4 9/6/3 10/6/2 11/6/1 Non- 29 28 29 3O 0 Aggression 30 29 30 30 0 Mutual 18 19 17 19 11 Defense 18 16 19 25 12 Coalition 28 27 28 29 1 Parity 29 23 30 30 1 Coalition 30 29 30 29 3 50/50 30 30 29 29 1 Table 26. Summary of Analysis of Variance on Data in Table 25 Source SS df MS F Between Groups 293.60 7 Alliance Types (A) 286.20 3 95.40 51.57* Groups within Alliance Types 7.40 4 1.85 Within Groups 3958.40 32 Game Tyne (8) 3390.75 A 847.69 529.81** AB 542.05 12 45.17 28.23** B x Groups within 25.60 16 1.60 Alliance Types Total 4252.00 39 **p < .001 *p < .01 97 comparison t-test indicated that there was a significant difference in the mean prOpensity for the strongest player to make a contact between the 11/6/1 and 10/6/2 games in each alliance condition (non-aggression, t=23.81; mutual defense, t=.33; coalition (parity), t=22.62; coalition (SO/50), t=21.23; t'=6.96, a =.Ol). No significant differences in the prOpensity for the strongest player to attempt to form an alliance were noted between the 10/6/2 games and any of the other game types in any of the alliance conditions. In the mutual defense games the number of alliances resulting from the initial contacts further supported Hypothesis 7 with respect to strong alliances; however, the 20 weak alliances that were formed in the 11/6/1 mutual defense games questioned that support. A search for the reason that 20 weak alliances were formed in the mutual defense games indicated that they were a reflection of the unexpected propensity for the two weaker players to prefer their weaker Opponent as an alliance partner. That phenomenon was previously ackowledged as a rejection of Hypothesis 5 and is not considered a rejection of Hypothesis 7. The lack of alliances formed in the 11/6/1 non-aggression games coupled with the prOpensity for the two weaker players to prefer the stronger Opponent as an alliance partner in the 11/6/1 non- aggression games, tends to support such an interpretation. Hypothesis 12 was given further support by the fact that only five of the 60 possible alliances were formed in the 11/6/1 coalition (SO/SO) games and 10 out of 60 possible alliances were formed in the 11/6/1 coalition (parity) games. Table 27 reports the initial contacts for each player position in the 10/6/2 and 11/6/1 coalition (SO/50) and coalition (parity) games. 98 mo. v 00 .00. v 0:0 «eon.o «0mN.m m m: m .m «mw.N «N..N 0. 0m N. mm ««.m.m : mm «:N.N :m N. mm. .m MN .0:u.0: 00:0...< m.. .0 00:0:0w0cm 500:0: :0. um0hu~ .m NN omNom 06.0..060 :0:u:0: 00:0...< «kmo.N mo 00:0:000L: 500:0: :0. umohuN Nm N >“..0. c6.3.08 :003 0:0.um :00: 0:0:0m :00: 0:0:um x003 0:0:um :00: meccum :00: 0:0:um 00.0:u 0000:00 < :O.u.mO: c0>0.: .\m\.. NNoNO. 00>h 050w m050w A>u.:0mv :O.u..0oU 0:0 NomNQm. :O.u..000 .\o\.. 0:0 N\o\o. 0:0 :. :o.u.mO: .0>0.m :00: :0. muomu:OU .0.u.:_ .NN 0.00» 99 The number of AB, AC, and BC coalitions resulting from initial contacts in the 10/6/2 and 11/6/1 coalition (SO/50) and coalition (parity) games is reported in Table 28. The data in Tables 27 and 28 are relevant to Hypotheses 10, 11, and 12. Hypothesis 10 predicted that the two weaker players would prefer the strongest player as their alliance partner in both the 11/6/1 and 10/6/2 games. Except for the 10/6/2 game in the coalition (parity) condition, Hypothesis 10 was SUpported. In the lO/6/2 coalition (parity) games, player B displayed random behavior (Z=.95) and player C preferred his weaker Opponent as an alliance partner (Z=2.24, p < .05). For players 8 and C (Z=2.12, p < .05 and Z=2.63, p < .05 respectively) there was a significant prOpensity to contact the strongest player in the 11/6/1 coalition (parity) condition. In the coalition (SO/50) 10/6/2 games players B and C revealed a significant prOpensity to contact the strongest player (Z=6.25, Z=6.51 respectively, p < .001). For the 11/6/1 games a similar propensity was manifest (Z=5.29, p < .001 for B and Z=6.30, p < .001 for player C). Hypothesis 11, that at the veto point the strongest player prefers to form an alliance with the weakest player in the coalition (parity) games and has no preference in the coalition (50/50) games was strongly supported by the initial contact data. In the coalition (SO/50) games the strongest player contacted his stronger opponent 27 times and his weaker Opponent 31 times which did not reject the hypothesis of random behavJor (Z=.13). In the coalition (parity) games the assumption of random behavior for player A's contact prOpensities was rejected (Z=7.03, p < .001). 100 Table 28. The AB, AC, and BC Alliances Resulting from Initial Contacts in the 10/6/2 and 11/6/1 Coalition (Parity) and Coalition (SO/50) Games Game Type 10/6/2 11/6/1 Alliance Type AB AC BC AB AC BC Coalition l l7 18 I l 8 Parity Coalition 25 30 0 2 0 3 50/50 101 Results Relevant to a Reduction of Conflict Behavior. One of the state purposes of the present experiment was to determine whether any of the manipulations examined did, in fact, result in a reduction Of conflict behavior. Three aspects Of the data--the observed probability of attacking given the Opportunity to attack, the mean number of attacks per game, and the probability of survival-~were considered to provide some measure of the level of conflict behavior. Each of those three aspects of the data were examined separately and are presented below. Table 29 presents the probability of attacking given an Opportunity to attack for each player position, by game type, alliance condition, and conflict type (the pure truel games, the pass-option games, and the alliance games). A 4x6x3x3 analysis of variance with repeated measure on three factors was computed on that data so that the simple effects could be thoroughly analyzed by means of Scheffe's multiple comparison t~tests. A summary of that analysis of variance is reported in Table 30. The data were ordered such that there were no significant differ- ences in the probability of attacking given the opportunity to attack as a function of Alliance Type or Player Position. There were sig- nificant effects for Game Type (F=3.107, p ==.O3l) and Conflict Type (F=8.642, p-=:.OIO as well as a significant Game Type by Conflict Type interaction (F=3.283, p-==.OO3). The Game Type by Player Position interaction and the Game Type by Conflict Type by Player Position interaction were also significant (F=6.098, F=3.774 respectively, p < .0005). Scheffe's multiple comparison t-tests suggested that the sig- nificant difference for game type was a function of the difference between the 6/6/6 games and the lO/6/2 games in the pass Option 102 mm. mm. oo.. Nm. om. 0.. mN. mm. mm. mN. N0. 0.. .000..... . Nm. 0.. 00.. 0N. mm. mm. .0. mm. mm. mm. om. mm. 06.0.0 000. 0 oo.. oo.. 00.. 00.. o... 00.. oo.. oo.. 00.. 06.. 00.. oo.. .03.. 0.3. .. mm. 00.. oo.. mm. 0.. Nm. .0. mm. mm. Nm. 0.. mm. ..000..... N mm. 8.. mm. 8.. mm. mm. mm. mm. mm. mm. mm. mm. no.0... 000. 0 oo.. oo.. 00.. 00.. oo.. 00.. 00.. oo.. 00.. oo.. .0.. oo.. .03.. 0.3. 0. mm. 00.. oo.. Nm. mm. .m. mm. 0.. mm. 0.. 0.. mm. 00:0...< M Nm. Nm. mm. 0.. 0.. Na. 00. Nm. Nm. om. .m. om. 00...: 000. 0 oo.. oo.. oo.. oo.. oo.. o... oo.. 00.. oo.. .0.. oo.. oo.. .03.. 0.3. m 0.. oo.. oo.. Nm. 0.. 00. Nm. mm. Nm. .0. mm. .m. B00..... 0 N0. 0.. .0. 0.. 0.. .0. m0. 0.. «0. N0. .0. N0. 00.0.0 ..0. 0 oo.. oo.. oo.. oo.. oo.. oo.. oo.. 00.. oo.. 00.. oo.. 00.. .03.. 0.3. 0 mm. Nm. mm. mm. Nm. mm. Nm. mm. Nm. mm. mm. mm. 8:0. . .< m Nm. Nm. mm. 0.. N0. 0.. mm. mm. Nm. 0:. mm. mm. 56.0.0 000. 0 o... 00.. oo.. o... oo.. oo.. 00.. 00.. 00.. oo.. 00.. 00.. .03.. 0.3. N mm. Nm. mm. mm. mm. ..m. Nm. Nm. mm. mm. mm. :N. 00:02.... 0 cm. Nm. om. N... 0... N0. 0:. N... 0:. ..0. N... N... :03... 000. 0 oo.. oo.. oo.. oo.. oo.. 00.. 00.. 00.. oo.. oo.. o... o... .03.. 0.3. 0 0 m < 0 m < 0 m < u m < / .uwwwmou mum” om\om >0..0. :O.mm0.mm< 0mc0w0a . 1| :O.u..00u :o.u..00u 1:02 .0303: :o.u.mO.1uW 0.. 0 . 0000.... :00»u< cu >u.::u.o:0o :0 :0>.w 0:.xumuu< mo >0...0000.. .mN 0.005 103 Table 30. Summary of Analysis of Variance for P(Attacking/Opportunity) Approximate Source SS df MS F Significance Within Groups .534 7 Alliance Type (A) .168 3 .056 .612 .642 A x Groups .366 4 .092 Between Grogps 2.033 424 Game Type (B) .141 5 .028 3.107 .031 AB .059 15 .004 .437 .947 AB x Groups .181 20 .009 Conflict Type (c) .412 2 .221 8.612 .010 AC .109 6 .018 .712 .651 AC x Groups .205 8 .026 Player Position (D) .017 2 .009 2.368 .156 AD .010 6 .002 .446 .830 AD x Groups .029 8 BC .123 10 .012 3.283 .003 ABC .069 30 .002 .616 .941 ABC x Groups .150 40 .004 BO .103 10 .010 6.098 < .0005 A80 .045 30 .001 .889 .627 ABD x Groups .067 40 .002 CD .015 4 .004 2.343 .099 ACD .027 12 .002 1.418 .253 ACD x Groups .026 16 .002 BCD .068 20 .003 3.774 < .0005 ABCD .074 60 .001 1.368 .095 ABCD x Groups .072 80 .001 Total 2.567 431 104 condition (t=6.94, t'=5.89, a =.Ol). There were no other significant differences in the probability of attacking given the Opportunity to attack as a function of game type in the pure truel, pass option, or alliance games. The significant difference between conflict types was a function of the difference between the pure truel and pass option 6/6/6 games (t=7.67, t'=5.89, a =.Ol). There were no other significant effects as a function of conflict type. Table 31 reports the mean number of attacks per game for each player position, in each game type within each of the four alliance conditions for the three conflict types. A 4x6x3x3 analysis of variance similar to that computed on the probability of attacking given the Opportunity to attack, was computed on the mean number of attacks per game. A summary of that analysis is presented in Table 32. A significant main effect for Game Type (F=132.l98, p < .0005) and for Conflict Type (F=492.938, p < .0005) as well as significant interactions between Game Type and Conflict Type (F=40.428, p <.0005) and Alliance Type by Game Type by Conflict Type (F=2.306, p = .007) were indicated. In addition there was a Game Type by Player Position and Game Type by Conflict Type by Player Position interaction (F=5.024, F=3.l44 respectively, p < .0005). Scheffe's multiple comparison t-tests were again used to examine the relevant simple effects. Table 33 presents the mean number of attacks per game for each game type in the three conflict types for each of the four alliance conditions. In the pure truel and pass option situations, there was no difference between the mean number of attacks per game between the 6/6/6 and 7/6/5 games, the 7/6/5 and 9/6/3 games, the 9/6/3 and 8/6/4 games, and the lO/6/2 and 11/6/1 105 m..m N..m m..m Nm.N mm.N No.m o0.N mm.N mo.m mm.N 0m.N mo.m 0600...< . mm.N w..N mo.m Nm.N mm.N no.0 om.N 00.N No.0 .0.N NN.N Nm.N 06.0.6 000. 0 mo.m mo.m mo.m 0o.m 0o.m 0o.m 0o.m 0o.m 0o.m mo.m mo.m mo.m .03.. 0.3. .. om.N mm.N mm.N mm.N om.N 00.0 0N.N N..N mm.N mm.N mm.N 00.0 0600...< N No.0 ...0 06.0 m..m N..0 6..m 66.0 No.m no.0 mm.N N..N Nm.N 06.0.0 000. 0 m..m m..m m..m m..m m..m m..m 00.m 00.0 06.0 mo.m mo.m 00.0 .03.. 0.3. o. o0.m m0.m m0.m mw.m Nw.m mm.m wo.m no.0 mm.N 6... mm.m m0.m 800..... m mm.m mm.m m0.0 .N.0 ...0 N..0 .N.m mN.0 mo.0 Nm.m 60.0 mm.m 06.0.0 000. 0 N..0 Nm.m N..m Nm.m Nm.m N..0 ...m ...0 ...m Nm.m Nm.m ...m .03.. 0.3. m .0.N mN.N mm.N no.0 No.m we. mm.N Nm.N mm.N No.m Nm.m No.0 0600...< 0 NN.m mm.m N0.m N0.m N0.m N0.m N0.m 00.0 NN.m N0.m mm.m N0.m 06.6.0 000. 0 N..0 N0.m N0.m NN.0 NN.0 NN.m No.0 N0.m N0.m 00.0 00.0 00.0 .03.. 0.3. w mo.m N..N No.0 mo.m N0.m om.N 00.m No.0 oo.m Nm.m o0.m N0.m 0600...< m NN.0 NN.0 oN.0 No.0 mm.m m..0 mm.m oN.0 no.0 N:.m mo.0 Nm.m 06.0.0 000. 0 0N.0 0N.0 0N.0 m..0 m..0 ...0 N..0 N..0 N..0 ...0 ...0 ...0 .03.. 0.3. N o..m No.m mo.m N..N 00.N mm.N Nm.N wm.N mm.N 00.. .0.m NN.0 0600...< 0 MN.0 6..0 MN.0 ...0 00.0 00.0 MN.0 NN.0 .N.0 60.0 mm.0 .N.0 06.6.6 000. 0 00.0 N0.0 N0.0 0m.0 00.0 0m.0 ...0 mm.0 ...0 ...0 ...0 Nm.0 .03.. 0.3. 0 0 m < 6 0 < 6 0 < 0 0 < ,//r .6wmwmou mew omNOm >0..0. :O.mm0.mm< 00:0.00 :Owu.mo. .0»0.. :O.u..0Ou :o.u..00u 1:02 .0003: 00x5 00:0...< 050w .0. mxumuu< .0 .00532 :00: ..m 0.00. 106 Table 32. Summary of the Analysis Attacks Per Game of Variance on Mean Number of Approximate Source SS df MS F Significance Within Groups 1.286 7 Alliance Type (A) .769 3 .256 1.983 .259 A x Groups .517 h .129 Between Groups 103.028 02h Game Type (8) 70.022 5 10.004 132.198 < .0005 AB 2.053 15 .137 1.292 .292 AB x Groups 2.119 20 .106 Conflict Type (C) 36.403 2 18.201 492.938 < .0005 AC 1.905 6 .317 8.598 .OOh AC x Groups .295 3 .037 Player Position (D) .203 2 .101 2.079 .188 AD .151 6 .025 .517 .782 AD x Groups .390 8 .0h9 BC 18.522 10 1.852 00.428 < .0005 ABC 3.170 30 .106 2.306 .007 ABC x Groups 1.833 40 .046 80 1.082 10 .108 5.020 < .0005 ABD .588 30 .020 .910 .601 A80 x Groups .862 #0 .022 CD .211 h .053 2.127 .125 ACD .385 12 .032 1.292 .311 ACD x Groups .398 16 .025 BCD .817 20 .041 3.100 < .0005 ABCD .980 60 .016 1.258 .168 ABCD x Groups 1.039 80 .013 Total lhh.7lh #31 107 Table 33. Mean Number of Attacks Per Game for Game Type and Conflict Type, Collapsed Over Player Position and Alliance Type Pure Truel Game Type 6/6/6 7/6/5 9/6/3 8/6/h 10/6/2 11/6/1 Means 0.09 4.16 3.91 3.68 3.11 3.05 Pass Option Game Type 6/6/6 7/6/5 9/6/3 8/6/4 10/6/2 11/6/1 Means 0.29 0.08 3.97 3.69 3.07 2.80 Alliance Game Type 9/6/3 6/6/6 7/6/5 8/6/h 10/6/2 11/6/1 Means 3.49 3.12 3.10 3.02 2.92 2.82 Note.--Underlined means are not significantly different by Scheffe's multiple comparison t-test (t' 8 5.89, a = .01) 108 games. In both the pure truel and pass option situations the 10/6/2 and 11/6/1 games manifest a significantly smaller mean number of attacks per game than did any of the other game types (t=9.19 and t=10.00 respectively, t'=5.89, a =.Ol). A significant propensity for more attacks per game in the 9/6/3 games than in any of the other game types was noted in the alliance games (t=5.968, t'=5.89, a =.Ol). In the 6/6/6, 7/6/5, 8/6/“, and 9/6/3 games, a significant propensity for more attacks per game in the pass option (P0) and Pure Truel (PT) games than in the alliance (A) games was noted. In the 6/6/6 games tPT_A=22.10 and tP0_A=18.87; in the 7/6/5 game =17.10 and t =15.81; in the 8/6/h games t =10.65 and tPT-A PO-A PT-A tPO-A=]0'87; and in the 9/6/3 games tPT_A=6.77 and t =7.7h PO-A (t'=5.89, a =.Ol). There were no significant differences between the mean number of attacks per game in the pure truel and pass option situations in any game type and there were no significant differences between the mean number of attacks per game within each conflict type in the 10/6/2 and 11/6/1 games. Table 34 presents the probability of survival for players A, B, and C in each game type, within each of the four alliance conditions, for the three conflict types. A summary of a 4x6x3x3 analysis of variance with repeated measures on three of the factors computed on the probability of survival data is reported in Table 35. There was a significant main effect for Game Type (F=50.h96, p < .0005), Conflict Type (F=h60.l99, p < .0005), Player Position (F=18.h7h, p = .001), and Alliance Type (F=25.17h, p = .005). The Game Type by Alliance Type, Conflict Type by Alliance Type, Game Type by Conflict Type by Alliance 109 N0. N0. 00.. 00. 00. .0. N0. 00. 00. N0. 00. 00. 0000...< . N0. 00. 00. N0. 00. 00. N0. N0. 00. 00. N0. 00. 00.0.0 000. 0 N0. .0. 00. 00. .0. 00. 00. .0. 00. N0. N0. 00. .03.. 0.3. .. 00. .0. .0. 00. 0N. 00. .0. 00. .0. 00. N0. 0.. 0000...< N .0. 00. 00. 00. N0. .0. 00. 00. 00. 00. N0. 00. 00.0.0 000. 0 .0. N0. 00. 00. N0. .0. 00. N0. 0.. 00. N0. 00. .03.. 0.3. 0. .0. 00. 00. 0.. N0. 00. 00. 00. 00. 0.. 00. NN. 000....0 0 N.. N0. 0.. 0.. 0.. 0.. 0.. 0.. 0N. 0.. .0. 0N. 00.0.0 000. 0 .0. 00. ... 00. 00. 0.. 0.. 0.. 0.. ... 00. 0.. .03.. 0.3. 0 N0. 00. 00. N0. 00. 0.. 00. .0. 0.. 00. 0.. ... 0000...< 0 0N. N0. 0.. .N. .N. 0N. 00. 0.. N.. .N. 0.. NN. 00.0.0 000. 0 0N. ... 0.. 0N. 0N. 0.. NN. 0.. 0N. .N. NN. 0.. .03.. 0.3. 0 00. .0. N0. 00. 00. 00. .0. 00. 00. N.. 0.. N.. 0000...< 0 0.. 0N. ... 0.. 0.. 0.. NN. 0.. 0N. N0. 0.. 0.. 00.0.0 000. 0 0N. NN. 0.. .0. 00. 0.. 0N. .N. 0.. NN. 0N. 0.. .00.. 0.0. . 00. 00. .0. 0.. 00. 00. .0. 00. N0. N.. 0.. 0.. 0000...< 0 ... NN. 0N. NN. 0.. 09 NN. N.. 0.. 0.. NN. .N. 00.0.0 000. 0 0N. 0N. 0N. 0N. 0N. 0.. 0N. 0.. 0.. 0N. 0N. 0N. .03.. 0.3. 0 0 0 < 0 0 < 0 0 0. 0 0 < / .03.”...00 ”HM om\om >u..0. co.mmu.mm< oncomoo co.u..00u co.u..0ou 1:02 .0303: co.u.mo. .0»0.. 0mm. 0oc0...< .0>.>.30 .0 >0...0000.. .00 0.00. 110 Table 35. Summary of Analysis of Variance on P(Survival) Data Source 55 df MS F Approximate Significance __ Within Groups 1.068 7 Alliance Type (A) 1.014 3 .337 25.170 .005 A x Groups .054 h .013 Between Groups 35.379 42h Game Type (B) 1.181 5 .236 50.096 < .0005 AB .480 15 .032 6.839 < .0005 AB x Groups .090 20 .005 Conflict Type (c) 6.012 2 .006 h6b.l99 < .0005 AC 2.379 6 .396 60.565 < .0005 AC x Groups .052 8 .007 Player Position (D) 2.356 2 .178 18.474 .001 AD ‘ .545 6 .091 l.h2h .313 AD x Groups .510 8 .060 BC 1.505 10 .150 36.352 < .0005 ABC .811 30 .027 6.528 < .0005 ABC x Groups .166 00 .00h 80 12.953 10 .295 80.802 < .0005 A80 .530 30 .018 1.102 .383 ABD x Groups .601 40 .018 CD .050 4 .013 .163 .950 ACD .856 12 .071 .929 .507 ACD x Groups 1.236 16 .077 BCD .750 20 .037 2.055 .002 ABCD 1.060 60 .018 1.157 .270 ABCD x Groups 1.221 80 .015 Total 36.hh7 h3l 111 Type, Game Type by Player Position, and Game Type by Conflict Type by Player Position interactions were also significant (F=6.839, p < .0005; F=60.565, p < .0005; F=6.528, p < .0005; F=80.8h2, p < .0005; F=2.hss, p < .002 reSpectively). The simple effects for the Game Type by Conflict Type by Player Position interaction and for the Game Type by Conflict Type by Alliance Type interaction were examined by means of Scheffe's multiple comparison t-tests. Player A had a significantly greater probability of survival in the 11/6/1 game than any other game type in the mutual defense (MD), coalition parity (CP), and coalition 50/50 (00) conditions (tMD=lO.56, tcp=10.99, t'10.56, a =.Ol; tC3710'00’ t'9.90, a =.05). Player A also had a significantly greater probability of survival than players 8 or C in the 11/6/1 game for all alliance types (t=1338.03, t'=10.56, a =.Ol). There were no other significant differences in the probability of players A, B or C surviving. There was a significantly greater probability of at least one of the players surviving in the alliance games for the non-aggression (NA), coalition parity, and coalition 50/50 conditions in the 6/6/6 through 10/6/2 games (tNA= 11.92, =10.62, th} t'10.56, a =.01; tcp=10.hl, t'9.90, a =.05). No significant differences for alliance type or conflict type were indicated in the 11/6/1 games and no significant differences for conflict type were indicated in the mutual defense condition. Discussion. The potential uelative conflict games were designed to examine the strategies employed in conflict situations that could be terminated by c00peration. In the pass Option games the terme- nation of the game required the simultaneous c00peration of all 112 surviving players. Two factors stood in the way of such c00peration; (1) since simultaneous c00peration was required, and feedback con- cerning responses was not received until after a response commitment had been made, some amount of trust necessarily precluded the choice of a cooperative strategy, and (2) the immediate goal, to obtain some portion of the 100 points payoff, was not necessarily compatible with the long range goal, to obtain the $1.50 per hour bonus for accumulating the most points in a six hour bonus period. The data supported the hypothesis that the subjects would exhibit an inverse relationship between the propensity to pass and disparity of relative strengths in the pass option games. The SUpport for that hypothesis was qualified somewhat by the fact that the lowest mean probability of attacking (1 - the highest probability of passing) was .83. Thus, even though the probability of passing increased as the disparity of relative strengths decreased from the veto point to the all equal point, there was a propensity to attack across that same range on the diSparity of relative strengths continuum. In the all equal pass option games, the prOpensity to attack given the opportunity to attack was significantly lower than the propensity to attack in the all equal pure truel games which forced attacks. In general, the mean number of attacks per game decreased as the disparity of relative strengths increased in all situations. However, the fact that there was no significant difference between the mean number of attacks per game in the pure truel and pass Option games, and that there was no significant effect reflected by the probability of attacking given an opportunity to attack as a function of the disparity of relative strengths, suggests that the effect over the 113 diSparity of relative strengths continuum is a function of the total moves required to end a game. As the diSparity of relative strengths increases, the total moves required to end a game decreases. The failure to obtain a reduction in conflict behavior would suggest that given limited communication and a history of conflict, the strategy Of resolving conflict situations through COOperative behavior is not often employed. Moreover, given the need for total cooperation from all participants and an incompatibility Of goals, it is probable that the participants in such situations would choose conflict as a means of terminating the situation. The reduction in the mean number of attacks per game in the alliance situations suggests that, given added means of communica- tion, the level Of conflict behavior may be lowered. However, since there was no significant reduction in the probability of attatking given the opportunity to attack as a function of alliances, such a hypothesis is questionable. It is conceivable that a fewer number of attacks is required to end a game in the alliance situations since the two alliance partners coordinate attacks against the isolate. Thus, the prOpensity for conflict behavior may not be reduced, it may merely be limited by the rules governing the situation. For example, the present study suggested that a propensity to attack one's alliance partner once the isolate was eliminated existed in the mutual defense games. It is likely that the reduction in conflict behavior in the alliance conditions which required one to honor an alliance after the isolate was eliminated was a function Of the lack of an Opportunity to resort to conflict behavior. In essense, it appears that, given incompatible payoffs and that the probability llh of obtaining one's payoff through conflict is available, conflict behavior will result. Such an assumption gains further support from the fact than an increase in the probability of at least one player surviving was evident in those alliance games in which the alliance partners were forced to honor the alliance after the isolate was eliminated. NO such increase in the probability of at least one player surviving was noted in the alliance games in which the alliance partners could attack each other once the isOlate was eliminated. Another interesting note concerning the probability of survival is that with one exception none of the player positions had a significantly greater probability of surviving than any of the other player positions. That one exception was that the dictator in the dictator situation will survive in almost every case. This would suggest that the notion of power inversion is not supported in the truel. Rather than supporting Shubik's (l95h) hypothesis that in the truel it does not pay to be slightly stronger than the other participants, it suggests that it does not pay to enter into a truel unless one is strong enough to guarantee that one cannot lose. The mutual defense and non-aggression alliance games were designed to examine the effect of trust on the preferred alliance partners. It was predicted that below the veto point in the mutual defense games the most preferred partner would be the Opponent who could do the least damage once the isolate was eliminated. In the non-aggression games, on the other hand, it was predicted that the preferred alliance partner would be the Opponent who could do the most damage if he remained the isolate. Both of these predictions 115 were supported in the 7/6/5 and 9/6/3 games; however, both of them failed to gain support in the 8/6/4 game. In both the mutual defense and non-aggression 8/6/h games the initial contact data was ordered in the predicted direction but the disparity of contact choices was attenuated such that the probability of the distribution being obtained by chance was between .10 and .20 for both conditions. The question that cannot be answered by the data from the present study is, what caused the attenuation of the effect in the 8/6/0 game? To answer that question will require further research aimed at first discovering if the effect is replicable. If the effect proves to be replicable, it will then be reasonable to focus research on its cause or causes. At the veto point and above it was predicted that the effect of trust would be overcome by the desire to win, and that the strongest Opponent would be the preferred alliance partner of both of the weaker Opponents in the non-aggression and mutual defense games. The data strongly SUpported that prediction in the non-aggression games but was equally strongly rejected in the mutual defense games. In fact, in the mutual defense games, there was a significant preference for the weaker Opponent which appeared to be a function of a belief that the stronger opponent would not honor an alliance once the isolate was eliminated. Consideration of that contradictory result indicates that trust or the lack of trust is still the major variable Operating at the veto point and above. If one of the weaker players forms an alliance with the strongest player, he must trust the strongest player not to eliminate him once the isolate is eliminated. That is, if an alliance is formed with the stronger Opponent at the veto point, 116 once the isolate is eliminated, the stronger player would have complete control over the allocation of the 100 points payoff. Data from the present eXperiment indicates that it is probable that the strongest player would take advantage of such a situation to add the 100 points to his point total. Thus, with long range goals in mind, alliances are formed between the two weaker opponents, which insures an outcome no worse-than the status quo. The data from the dictator situation reflects the same line of reasoning. In the non-aggression games the weaker players both preferred the strongest opponent since the only way to insure that some portion of the 100 points payoff was obtained was to form an alliance with the dictator. If the dictator chose not to form an alliance, the most that could be lost was the effort required to push the contact button. On the other hand, if the dictator chose to form an alliance some portion of the 100 points payoff would be gained. In the mutual defense game, the probability of either of the weaker players gaining some portion of the 100 points payoff was low. If they contacted the dictator and he reciprocated, they still had to complete the game hOping that once the isolate was eliminated, the dictator would not choose to eliminate his alliance partner. Since the strongest player often chose to contact the stronger of his two Opponents when he did make a contact, it was reasonable to assume that he wanted to negate the power of his strongest Opponent during the alliance phase of the experiment, and eliminate him once the isolate had no points remaining. Thus, unless the weaker players trusted the strongest player, it was reasonable to either choose not to form an alliance or to form one with the weaker Opponent. Since 117 the contact phase of the game lasted one and one half minutes if the players choose not to form an alliance, and only the length of time it took to make a reciprocal contact if the two weaker players formed an alliance, the time spent in the situation was shortened con- siderably by forming an alliance. Moreover, the outcome was probably not changed. With the exception of Caplow (1959) the concept of trust has been virtually ignored in alliance formation research. It has been commonly accepted that, given the chance to form alliances, alliances will inevitably be formed. Caplow's hypothesis that in the terminal situation alliances will not be formed, was supported by the difference between the number of alliances formed in the non-aggression and mutual defense games. In the 7/6/5 games there were AS non-aggression and 16 mutual defense alliances formed, in the 8/6/4 games there were 58 non-aggression and 17 mutual defense alliances formed, and in the 9/6/3 games there were 59 non-aggression and 7 mutual defense alliances formed. A chi-square which tested the hypothesis that there was no difference in the number of alliances formed in the non-aggression and mutual defense games strongly rejected that hypothesis (X2=77.l7, df=2, p < .001). Thus, the data indicated a significant propensity to form fewer alliances in the mutual defense games (the terminal situation) than in the non-aggression games. The combined data examining the mutual defense and non-aggression games was considered as support for the hypothesis that trust is an important variable in the consideration of alliance partners as well as the decision to form alliances. Although the present study did not pretend to fully explore all of the possible ramifications Of trust, the results did point out 118 that trust is an important variable in alliance formation. One of the major focuses of the present experiment was a test of the parity principle. The parity norm as postulated by Gamson (1961a) states that the participants in an alliance situation would eXpect the other participants to demand a share of the payoff that is prOportionate to the share of the resources they contribute to the coalition. Subsequent research (e.g., Gamson, l96lb; Chertkoff, 1960; Phillips and Cole, 1970) has tended to support the theory that the parity norm has a major role in determining preferred alliance partners; however, there seems to be a complete lack of published research which has directly tested the parity norm. The present experiment directly tested the parity principle by forcing a parity split of the payoff in one condition and forcing a 50/50 Split of the payoff in another condition. Previous research on alliance formation in situations similar to the 7/6/5, 8/6/h and 9/6/3 games--situations in which A > B > C and A < (B+C)--has generally reported a propensity to form alliances as exemplified by the data from Vinacke and Arkoff (1957) and Chertkoff (1966). The Vinacke and Arkoff and Chertkoff data and the data from the coalition (parity) condition of the present eXperiment is pre- sented in Table 36. It has been considered reasonable to assume that, in general, data from previous research has indicated support for the assumption that the parity norm ”causes” the distribution of alliances to be ordered as in the Vinacke and Arkoff, and Chertkoff data. The data from the present eXperiment casts doubt on the validity of such an assumption. Below the veto point, the data from the present experiment 119 Table 36. Distribution of Alliances as Reported by Vinacke and Arkoff (I957), Chertkoff (1966), and the Coalition (Parity) and Coalition (SO/50) Conditions in the Present Study Alliance Type AB AC BC Vinacke and Arkoff 9 20 59 Chertkoff l 9 1h Coalition (Parity) 3 3 107 Coalition (SO/SO) 42 28 75 x§=2.59 x§=hh.54 x§=ls.7h df=2 df=2 df=2 p<.001 p<.001 X2 tests the hypothesis that there is no difference between the distribution a of alliances formed in the Vinacke and Arkoff and the Chertkoff data. X tests the hypothesis that there is no difference between the distribution of alliances formed in the combined Vinacke and Arkoff and Chertkoff data and the data in the coalition (parity) condition. X tests the hypothesis that there is no difference between the distribution of alliances formed in the combined Vinacke and Arkoff and Chertkoff data and the data in the coalition (SO/50) condition. 120 showed strong support for the proposition that the weaker Opponent would be preferred alliance partner in the coalition (parity) condition. Moreover, the propensity to form weak alliances was such that it was not necessary to analyze the results statistically. Weak alliances were formed in virtually every case. To determine whether there was a difference between the data from the present study and previous studies, a chi-square was first computed to test the hypothesis that there was no difference between the data from the present study and previous studies, a chi-square was first computed to test the hypothesis that there was no difference between the Vinacke and Arkoff data and the Chertkoff data with respect to the distribution of alliance types formed. That chi-square did not reject the null hypothesis (X2=2.59, df=2). A chi-square which tested the hypothesis that there was no difference between the combined Vinacke and Arkoff and Chertkoff data, and the data from the coalition parity games strongly rejected that hypothesis (X2=hh.5h, df=2, p < .001). Thus, the relevancy of the parity norm with respect to alliance formation is questionable. If the formation of weak alliances is a function of the parity norm, why is the propensity to form weak alliances significantly greater in the present experiment when a parity division of the payoff is forced, than it has been in previous eXperiments in which a parity division of the payoff was available but not required? Another problem with respect to support for the parity norm occurred vhen the coalition (SO/50) data was considered. There was a non-significant preference for the weaker opponent in the 8/6/h and 9/6/3 games and a significant preference for the weaker Opponent in the 7/6/5 games. In the 7/6/5 and 9/6/3 games the distribution 121 of alliances formed was not random and a similar but non-significant result was observed in the 8/6/h game. Weak alliances were the most preferred, followed by strong alliances and medium strength alliances in that order. The preference for weak alliances in the coalition (SO/50) condition coupled with the very strong propensity for weak alliances in the coalition (parity) condition questions the viability of the hypothesis that the parity norm is the basis of the formation of weak alliances. It should be noted, however, that although weak alliances were preferred in the coalition (SO/50) condition, the distribution of alliances was significantly different from the distribution of alliances reported by the combined Vinacke and Arkoff and Chertkoff data (x2=l5.7h, df=2, p < .ool). Thus, it appears that the Vinacke and Arkoff and Chertkoff data and the coalition (SO/50) data do not reflect the same alliance preference. An eXplanation of the results which might account for the uneXpected non-random preference for alliances in the coalition (SO/SO) condition has been prOposed by Caplow (I968). Caplow noted an unusual result in the Vinacke and Arkoff (1957) all equal game. Vinacke and Arkoff labeled their players A, B, and C and reported that in the all equal game there was a non-significant preference for BC, AB, and AC alliances in that order. Caplow suggested that the propinquity of the letters was used as a cue to determine which alliances would form. It is possible that the same effect might have occurred in the present eXperiment by using the prOpinquity of the numbers as cues for forming alliances. For example, in the 7/6/5 game, 7,6 or 6,5 alliances would be preferred. Since any alliance that formed would win, and the 100 points payoff was to be evenly divided, it is not 122 unlikely that such was the case. If we consider Caplow's interpretation of Vinacke and Arkoffs results to be valid, and apply it to the present study, it would account for the non-random preference for alliances in the coalition (SO/50) games; however, it would not account for the high probability of forming weak alliances in the coalition (parity) games. It is conceivable that the strong preference for weak alliances in the coalition (parity) games was a function of the fact that the forced parity split of the payoff was a much stronger manipulation than the effect Of the parity norm which is based on the subjective interpretation of the situation by each subject. The present study has examined the effect of a strong parity principle on the preference for alliance partners as well as the effect of the absence of a parity norm. To truly test the parity norm as proposed by Gamson it will be necessary to find a means of measuring and manipulating the subjective estimation of the strength of the parity norm by the participants in an alliance situation. With the exception of the predicted behavior of the two weaker players in the lO/6/2 coalition (parity) games, the predictions following from the parity principle were surprisingly accurate at the veto point and above. In the 10/6/2 coalition (parity) games, player C preferred his weaker Opponent as an alliance partner and player B had no preference. One possible interpretation of such behavior is that if a BC alliance is formed in the lO/6/2 game there will be no survivors and the accumulated points remains the same for all players. On the other hand, if any other alliance forms, the strongest member of that alliance will gain relative to the other 123 two players. If the weakest player forms an alliance with the strong- est player he gains relative to the medium strength player but he loses relative to the strongest player. A similar fate faces the medium strength player should he form an alliance with the strongest player; however, the relative gain of the strongest player over the medium strength player is less than the gain of the strongest player over the weakest player. As a result, the medium strength player is hard pressed to make a decision and appears to behave randomly. On the other hand, the decision is less difficult for the weakest player who prefers the status quo to aiding the strongest player at his own eXpense. The strongest player follows the predictions based on the parity principle and reveals a strong preference for the weakest player as an alliance partner in the coalition (parity) games. The problem of relative gain does not enter into the decision process in the 10/6/2 coalition (SO/50) games. Since a winning alliance must include the strongest player, both weaker players prefer the strongest player as an alliance partner. 0n the other hand, the strongest player exhibits a random preference, since any alliance he enters will win. Conclusion The purpose of the present study was threefold. First, it was to test a model of strategy selection in the uelative conflict situation which has been prOposed by Cole and Phillips (1969); second, it was to examine the strategies employed in potential uelative conflict situations; and third, it was to examine potential uelative conflict situations in which alliances are allowed. An additional reason for the study was to determine whether providing a means for terminating a situation through cooperative behavior would lower the level of conflict in a situation that would, otherwise, have been characterized by intense conflict. With respect to the Cole and Phillips model, the data suggested that the model should be rejected. However, it was evident that the model should not be discarded. Although, the model did not offer a ”good” fit by statistical criterion, it did appear to offer a reasonable prediction of each of the participants attack preferences. It appeared that to rectify the failure to meet the statistical criterion for goodness of fit, the model would need a reassessment of some of its basic assumptions. It was suggested that one probable candidate for revision is the importance of R(X) in the determination of threat. It appears that a reweighting of R(X) could account for much of the discrepancy between the predicted and Observed attack preferences on moves following the initial move of the game. Morespecifically, the reweighting of R(X) appears to be necessary for those situations in which both R(X) and D(X) are varied for all pdayers. The observed behavior in the potential uelative conflict situations suggested that merely providing a means for terminating a 12h 125 conflict situation by cOOperative behavior is not sufficient to reduce the level of conflict. No difference was noted in the pro- pensity to attack in the pure truel, pass Option, or alliance games. There was a significant propensity for at least one of the players to survive in the alliance games in which the alliance partners were forced to honor the alliance until the game ended. The increase in the probability of at least one player surviving in those alliance conditions was probably a function of the fact that it was easier to arrange for two players to survive in the alliance games than in the pass Option games. It was possible for two or three players to survive in both the pass Option and alliance games; however, there were virtually no cases in which all three players survived and very few cases in which two players survived when an explicit alliance was not allowed. Thus, it appears that given incompatible goals, limited communication, the need for complete trust in your Opponent, and a means by which a situation can be terminated by conflict, the conflict strategy will be chosen. Given the same incompatible goals, an improved channel of communication, and a negation of the need to trust your Opponent a COOperative strategy is likely. The same incompatible goals and an improved channel of communication without a negation of the need to trust your Opponent, results in the selection of a quasi-COOperative strategy which deteriorates into a conflict strategy at the first chance. The present study indicated that alliances that are not binding seem to be a means to improve one's position in an attempt to obtain one's goal. Thus, since alliances in the real world cannot be 126 guaranteed binding, it appears that a balance of power may in fact be a necessary procedure to obviate uelative conflict. The present study would suggest; however, that as long as the goals are incom- patible, the balance of power will, at best, only temporarily alleviate the manifestation of conflict behavior. The next step in the research would seem to be to examine the prOpensity for conflict behavior in potential uelative conflict situations in which the goals are not necessarily incompatible. If it should prove to be the case that non-incompatible goals do in fact lower the probability of conflict behavior, then perhaps some means for redefining the goals of “Opposing” nations may negate the need for a balance of power. If the need for a balance of power can be set aside, the world may be oriented toward transforming a potential uelative conflict situation into a cooperative situation. LIST OF REFERENCES LIST OF REFERENCES Boulding, K. E. Conflict and Defense, New York: Harper and Row, 1963 Caplow, T. Further deveIOpment of a theory of coalition in the triad. Journal of Abnormal and Social Psychology, 1959, 65, 088-493. Caplow, T. Two Against One: Coalitions in Triads, New Jersey: Prentice-Hall, 1968. Chertkoff, J. M. The effects of probability of future success on coalition formation. Journal Of Experimental Social Psychology. 1966 ’ _2_9 265-277 0 Cole, S. G. The ”strength is weakness” effect in the truel. Paper presented at the meeting of the Midwestern Psychological Association, Chicago, May A, 1968. Cole, 5. G. An examination of the power inversion effect in three person mixed-motive games. Journal of Personality and Social Psychology, 1969, 11) 50-58. Cole, S. G. and Hartman, E. A. Situation ambiguity and label effects in social interaction experiments, in preparation. Cole, S. G. and Phillips, J. L. The propensity to attack others as a function of the distribution of resources in a three person game. Psychonomic Science, 1967, 2_(h), 239-2&0. Cole, S. G. and Phillips, J. L. An analysis of uelative conflict. Paper presented at the meeting of the Peace Research Society (International), Ann Arbor, November, 1969. Cole, S. G., Phillips, J. L., and Hartman, E. A. A General Model for Strategy Selection in Uelative Conflict Situations, in preparation. Coser, L. The Functions of Social Conflict, New York: The Free Press, 1964. Deutsch, M. and Krauss, R. M. Studies of interpersonal bargaining. Journal of Conflict Resolution, 1962, 6_(l), 52-76. Edwards, A. L. Experimental Design in Psychological Research, New York: Rinehart and Company, 1960. 127 128 £115, J. and Sermat, V. Cooperation and the variation of payoff in non-zero-sum games. Psyphonomic Science, 1966, A, lA9-150. Gamson, W. A. A theory of coalition formation. American Sociological Review, 1961a, 26, 373-382. Gamson, W. A. An experimental test of a theory of coalition formation. American Sociological Review, 1961b, 26, 565-573. Hartman, E. A. Label effects in social interaction experiments. Psychonomic Science, 1970a, 19_(A) 222-223. Hartman, E. A. Development and test of a model Of conflict in a truel. Unpublished Master's Thesis, Michigan State University, I970b. Hartman, E. A. and Phillips, J. L. A Random-walk model for uelative conflict. Report No. 69-2, COOperation/Conflict Research Group, Michigan State University, East Lansing, Michigan, 1969. McNemar, Q. Psychological Statistics, New York: John Wiley and Sons, 1957. Mendelsohn, G. A manual for the Laboratory Control Apparatus, (LCA), Human Learning Research Institute, Michigan State University. (in preparation). Nitz, L. H. and Phillips, J. L. The effects of divisibility of payoff on confederative behavior, Journal of Conflict Resolution, 1969, _1__3__9 381'387 o Phillips, J. L., Hartman, E. A., and Klein, M. Three random walk models for three-person conflict. Paper presented at the Mathematical Psychologists Conference, Indiana Univeristy, April, 1970. Phillips, J. L., Klein, M., and Hartman, E. A. Geometric representation for models of three-person conflict. Paper presented at the meeting of the Midwestern Society of Multivariate Experimental Psychologists, Cincinnati, May, 1970. Phillips, J. L. and Nitz, L. H. Social contacts in a three-person political convention situation. Journal of Conflict Resolution, 1968, 122 206-21A. Phillips, J. L. and Cole, S. G. Sex differences in triadic coalition formation strategies in J. L. Phillips and T. L. Conner (Eds.) Studies of Conflict, Conflict Reduction, and Alliance Fonmation, Report No. 70-1, COOperation/Conflict Research Group, Michigan State University, East Lansing, Michigan, 1970. 129 RapOport, A. Games which simulate deterrence and disarmament. Peace Research Reviews, 1967, l_(l), Canadian Peace Research Institute, Clardson, Ontario. RapOport, A. Prospects for experimental games. The Journal of Conflict Resolution, 1968, lg_(A), A6l-A70. RapOport, A. and Chammah, A. M. Prisoner's Dilemma: A Study in Conflict and COOperation, Ann Arbor: University of Michigan Press, 1965. RapOport, A. and Guyer, M. A taxonomy of 2 x 2 games. General Systems, 1966, ll! 203-21A. Richardson, L. F. Arms and Insecurity, Pittsburgh: Boxwood Press, 1960a. Richardson, L. F. Statistics of Deadly Quarrels, Pittsburgh: Boxwood Press, 1960b. Scheffe, H. A method for judging all contrasts in the analysis of variance. Biometrika, 1953, A0, 87-IOA. Schelling, T. C. The strategy of Conflict, New York: Oxford University Press, 1963. Sermat, V. and Gregovich, R. P. The effect of experimental manipula- tions on COOperative behavior in a chicken game. Psychonomic Science, 1966, A_(12), A35-A36. Shubik, M. Does the fittest necessarily survive in M. Shubik (Ed.), Readings in Game Theory and Political Behavior, Doubleday, 195‘1 ’ 113-1'16 o Shubik, M. Game Theory and Related Approaches to Social Behavior, New York: John Wiley and Sons, l96A. Shure, G. H., Meeker, R. J. and Hansford, E. The effectiveness of pacifist strategies in bargaining games. The Journal of Conflict Resolution, 1965, 9_(I), 106-117. Vinacke, W. E. and Arkoff, A. An eXperimentaI study of coalitions in the triad. American Sociological Review, 1957, 223 AO6-A1A. Willis, R. H., and Long, Norma Jean. An experimental simulation of an internation truel. Behavioral Science, 1967, 12) 2A-32. Wright, Quincy. The Nature of Conflict. The Western Political Quarterly, 1951, A, 193~209. APPENDIX EXPERIMENTAL MATERIALS 130 Instructions for the Pass Option Games At this time we are going to modify the rules of the game which you have been playing. Previously you have each been required to make an attack on one of the other players each time that your ready light came on. Starting with the next game that will no longer be a re- quirement. You will be allowed to choose not to attack either of the other players on a move, that is, you will have the option to pass on any move. To implement the pass Option we have set the apparatus so that you will have a 30 second decision period after your ready light comes on in which to make your attack choice or to pass. If you make an attack choice within that 30 seconds, your ready light will go out and the game will appear very similar to the previous games. If you choose to pass, your ready light will go out after 30 seconds. When all three players have attacked or when 30 seconds has elapsed, the score will be calculated and the next move will begin. Because of the new pass Option rule, the game must have an end if all three players decide to pass. Therefore, we have changed the rules of the game so that, if there are three players who have points remaining and all three players pass for three simultaneous consecutive moves the game will end. In those situations in which there are two players with points remaining, if both players pass for three simultaneous consecutive moves the game will end. In addition a game will end if seven decision periods have been completed regard- less of the points each player has remaining. The game will end in one Of A_ways. (I) There is a sole survivor in which case he receives the 100 points 131 for that game. (2) There are two survivors in which case they will divide the 100 points in direct proportion to the ration of the number of points they each have to the total number of points remaining. For example, if one player has 15 points remaining and another has five points remaining, the first player would receive 75 points and the second would receive 25 points toward the bonus for that time period. (3) There are three survivors, in which case they will divide the 100 points for that game as it was divided when there were two survivors. For example, if each player has 10 points remaining they would each receive 33 points toward the bonus for that time period. (A) There are no survivors, in which case none of the players would receive bonus points. Are there any questions? Instructions for the Non-Aggression Alliance Games At this time we are again modifying the rules of the game. The new rules state that if you choose to, you will be allowed to form an alliance before you begin the seven decision periods. At the beginning of each game you will be given three 30 second contact periods in which you may choose to indicate one of the other players as your de- sired alliance partner. You will indicate this choice by pressing the button switch under his name on your control box. If you do not choose to form an alliance, do not push any of the button switches. An alliance will be formed if two players make reciprocal contacts during the same contact period. If an alliance is formed, the contact process 132 will be terminated and the game will begin. Any alliance that is formed will be announced by the experimenter and the lights above both of the partners' names on their control boxes will be turned on. If no alliance is formed during the contact periods, the game will be played as the game with the pass option was played. If you form an alliance, you will be held to the terms of the alliance for the remainder of that game. The terms of the alliance state that you will not attack your alliance partner. You are not required to attack the third player if you choose not to. The 100 bonus points for each game will be distributed in direct prOportion to the ratio of the number of points the surviving player or players have remaining to the total number of points remaining. That is, the bonus points will be distributed in the same way that they were distributed in the pass option games. The distribution of the bonus points is not effected by the formation of an alliance except that if the two alliance partners are the only players re- maining they may not continue to attack each other. Are there any questions? Instructions for the Mutual Defense Alliances Games At this time we are again modifying the rules of the game. The new rules state that if you choose to, you will be allowed to form an alliance before you begin the seven decision periods. At the beginning of each game you will be given three 30 second contact periods in which you may choose to indicate one of the other players as your desired alliance partner. You will indicate this choice by pressing the button switch under his name on your control box. If you do not choose to form an alliance, do not push any of the button 133 switches. An alliance will be formed if two players make reciprocal contacts during the same contact period. If an alliance is formed, the contact process will be terminated and the game will begin. Any alliance that is formed will be announced by the eXperimenter and the lights above both of the partners names on their control boxes will be turned on. If no alliance is formed during the three contact periods, the game will be played as the game with the pass Option was played. If you form an alliance, you will be held to the terms of the alliance for the remainder of the game. The terms of the alliance state that while there are three players in the game, you will not attack your alliance partner. Furthermore, if the player who is not in the alliance attacks one of the members of the alliance, then both members of the alliance must attack that player on the next move. Except for the preceding case, you are not required to attack the third player if you choose not to. The 100 bonus points for each game will be distributed in direct proportion to the ratio of the number Of points the surviving player or players have remaining to the total number of points remaining. That is, the bonus points will be distributed in the same way that they were distributed in the pass option games. The distribution of the bonus points is not effected by the formation of an alliance. Are there any questions? Instructions for the Coalition Formation (Parity) Games At this time we are again modifying the rules of the game. The new rules state that if you choose to, you will be allowed to form an alliance before you begin the seven decision periods. At the beginning 13A of each game you will be given three 30 second contact periods in which you may choose to indicate one of the other players as your desired alliance partner. You will indicate this choice by pressing the button switch under his name on your control box. If you do not choose to form an alliance, do not push any of the button switches. An alliance will be formed if two players make reciprocal contacts during the same contact period. If an alliance is formed, the contact process will be terminated and the game will begin. Any alliance that is formed will be announced by the experimenter and the lights above both of the partners names on their control boxes will be turned on. If no alliance is formed during the three contact periods, the game will be played as the game with the pass option was played. If you form an alliance, you will be held to the terms of the alliance for the remainder of the game. The terms of the alliance state that you will not attack your alliance partner. You are not required to attack either of the other players if you choose not to. The initial distribution of the 100 bonus points will be in direct proportion to the ratio of the number of points that the surviving player, players, or alliance have remaining. If all three players survive or if one member of the alliance and the third player survive, the alliance will receive its share of the bonus points which will be determined by the number of points that the alliance has re- maining, and those points will be given to each member of the alliance in direct proportion to the number of points that each member of the alliance can remove. The third player would receive his share of the bonus points according to the number of points he had remaining. For example, if at the end of the game, one member of the alliance 135 had 2 points, the other had 6 points, and the third player had 8 points in the game in which each player could remove 6 points, the alliance would receive 50 bonus points, 25 of which would go to each of the member of the alliance. The third player would receive 50 bonus points. The same division of the bonus points would result if one member of the alliance was eliminated and the surviving alliance member and the third player each had 8 points remaining at the end of the game. If one member of the alliance is the sole survivor or if both members of the alliance are the survivors, then both members of the alliance will receive a share of the 100 bonus points which is in direct proportion to the number of points that they can remove. If the third player is the sole survivor, he will receive 100 bonus points. If there are no survivors, none of the players will receive bonus points. Are there any questions? Instructions for the Coalition Formation (SO/SO) Games At this time we are again modifying the rules of the game. The new rules state that if you choose to, you will be allowed to form an alliance before you begin the seven decision periods. At the beginning of each game you will be given three 30 second contact periods in which you may choose to indicate one of the other players as your desired alliance partner. You will indicate this choice by pressing the button switch under his name on your control box. If you do not choose to form an alliance, do not push any of the button switches. An alliance will be formed if two players make reciprocal contacts during the same contact period. If an alliance is formed, the contact process will be terminated and the game will begin. Any alliance that is formed 136 will be announced by the experimenter and the lights above both of the partners names on their control boxes will be turned on. If no alliance is formed during the three contact periods, the game will be played as the game with the pass Option was played. If you form an alliance, you will be held to the terms of the alliance for the remainder Of the game. The terms of the alliance state that you will not attack your alliance partner. You are not required to attack the third player if you choose not to. The initial distribution of the 100 bonus points will be in direct prOportion to the ratio of the number of points that the sur- viving player, players or alliance have remaining. If all three players survive or if one member of the alliance and the third player survive, the alliance will receive its share of the bonus points and half of those points will be given to each member of the alliance. The third player would receive his share of the bonus points according to the number of points he had remaining. For example, if at the end of the game, one member of the alliance had 2 points, the other had 6 points, and the third player had 8 points, the alliance would receive 50 bonus points, 25 of which would go to each of the members of the alliance. The third player would receive 50 bonus points. The same division of the bonus points would result if one member of the alliance was eliminated and the surviving alliance member and the third player each had 8 points remaining. If one member of the alliance is the sole survivor or if both members of the alliance are the survivors, both members of the alliance will receive 50 bonus points. If the third player is the sole survivor, he will receive 100 bonus points. If there are no survivors, none Of the players will receive bonus points. 137 The following IBM sense sheets were used to record the relevant data from the six game types. 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