M MOTWARONAL BASS OF SEX DEEEEENCES ME THE " PRISONER'S DILEMMA GAME Thesis fer the Degree of Phi Q. HERMAN STATE UNEVERSéW E. ALAN HRREWXN jaw-inf; LSIL r-vw '-'v: Ian-nae“ Date 0-7639 8 hm”; .. “y L . 7 All 9. state Lava-i: silty "37.5.“. This is to certify that the thesis entitled THE MOTIVATIONAL BASIS OF SEX DIFFERENCES IN THE PRISONER'S DILEMMA GAME presented by E. Alan Hartman has been accepted towards fulfillment of the requirements for Ph.D. degreein Psychology fl/cZMA/L 3i flied/04, Major professor August 17, 1972 ABSTRACT THE MOTIVATIONAL BASIS OF SEX DIFFERENCES IN THE PRISONER'S DILEMMA GAME By E. Alan Hartman A consistent finding in the research on the prisoner's dilemma game has been that males cooperate more than females when playing against a responsive other participant, while the reverse relationship has been found when playing against an unresponsive other. A theory based on the eXploitative-accommodative theory of Edgar Vinacke was _ developed to account for these results. The basis of this theory was that males and females enter game situations with different motivations: males try to maximize their own gain, while females try to maximize the joint gain and to be fair. The theory also makes different predictions for males and females with regard to their responses to the frustration of these motives: males respond by bargaining with the other partici- pant to gain a satisfactory outcome, while females simply try to leave the situation. Four different styles of play were developed for a simulated 0p- ponent to play against the subjects in this study. These four styles of play or strategies were: I) contingent (responsive) exploitative; 2) noncontingent (unresponsive) exploitative; 3) contingent accommoda- tive; and h) noncontingent accommodative. The revised exploitative- accommodative theory makes differential predictions for males and females playing against these four different strategies. Against a noncontingent cooperative strategy males should exploit the other, E. Alan Hartman while females should cooperate; while against any contingent strategy males should respond to the exploitativeness of the strategy, and females should try to leave the situation. An examination of the payoff matrix of the prisoner's dilemma game indicated at least five different motives for choosing the ”defect” alternative in the matrix. These five motivations were: i) maximize absolute gain; 2) minimize other's payoff; 3) minimize the risk in- volved in making a choice; A) maximize relative gain with reSpect to the other participant; and 5) attempt to control the other's choices using the payoff matrix. A six alternative matrix was developed to differentiate between these five different motivations for choosing ”defect” in the prisoner's dilemma. This study was designed to test the reviseanccommodative theory and to determine the motivations for choosing ”defect'I in a prisoner's dilemma. To accomplish this four factors were varied: l) the exploitativeness of the simulated other participant; 2) the reSpon- siveness (contingency) of the simulated other; 3) the sex of the sub- jects; and A) the size of the matrix. The results of the study gave only partial support for the revised exploitativewaccommodative theory. Several of the predictions were borne out. However, a nonsupportive result was that the females did not respond differentially to contingency of response but only to the exploitativeness of the response, with males continually preferring that alternative which maximized their own gain. In the six alternative matrix different l'defect" alternatives were chosen by males and females under different strategies. The most E. Alan Hartman prominent difference occurred for the ”maximize absolute gain” alternative with females choosing it more under exploitative strategies regardless of contingency than under accommodative strategies. Males, however, chose this alternative as a function of both the contingency and exploitativeness of strategy with more of these choices made under noncontingent cooperative than contingent and fewer made under a con- tingent accommodative strategy than a contingent exploitative strategy. THE MOTIVATIONAL BASIS OF SEX DIFFERENCES IN THE PRISONER'S DILEMMA GAME By E. Alan Hartman A THESIS Submitted to Michigan State University in partial fulfillment of the requirement for the degree of ‘ DOCTOR OF PHILOSOPHY Department of Psychology I972 £3 ACKNOWLEDGMENTS The author would like to express his appreciation to Dr. James L. Phillips for his help In the preparation of this dissertation and for his guidance over the preceding four years of study. Thanks is also due to Dr. Lawrence Messé for his consistently generous help and suggestions before and during this study. Dr. Thomas Conner, Dr. Leighton Price, and Dr. William Crano also.made significant contributions to the design and writing of this study. Special recognition goes to Bruce Currie and Lawrence (Kip) Burgoyne for their help in running subjects. Mrs. Pat Spellicy, Miss Sue Eareckson, and Mrs. Peggy Smith typed and corrected the entire volume. Without these five people this dissertation would not have been completed in l972. Behind every piece of work of this nature there is a woman whose patience and encouragement make it all possible and worth- while; this dissertation is no exception. The author would like to thank his wife for her faith and understanding during the prepara- tion and completion of this piece of work. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES Chapter INTRODUCTION Theoretical Approaches Game Theory Behavior Theory Application of the Theories to the Prisoner's Dilemma Payoff Matrix Characteristics Mechanisms of Decision Making Review of Sex Differences Males C00perate More than Females Females Cooperate More than Males Definitive Studies No Sex Differences Found Definition of Problem and A PrOposed Solution Payoff Matrix Test of the Theory Hypotheses METHOD Subjects Setting Design Strategies Apparatus and Materials Procedure Session One Session Two Subjects Per Session Two Choice Session The Six Choice Session Iii ll l3 I6 18 20 2A 27 3] 33 35 an 47 SO 50 so 53 53 58 6O 62 62 63 66 iv Chapter RESULTS Analyses Performed Preliminary Results General Analysis Results of Test of Theory Sex Differences General Results DISCUSSION \ Sex Differences Comparison to Previous Results Implications for Theory General Results Boundary Conditions Hypotheses Not Related to Sex Effect of Matrices LIST OF REFERENCES APPENDIX A: Questionnaire APPENDIX B Instruction Booklet I Instruction Booklet 2 APPENDIX C Instruction Booklet l Instruction Booklet 2 Instruction Booklet 3 Instruction Booklet A APPENDIX D Results on Boundary Conditions Discussion of Preliminary Results APPENDIX E The Analysis on Percent Cooperation Page 70 70 7i 8] 81 95 Ill Ill Ill ll3 IIS lIS ll6 ll7 I2] 124 l3h 13% I36 I37 137 IAO IA3 lhh lh6 lh6 156 l6h 16h TABLE l2 13 IA LIST OF TABLES The general two person, two choice situation Examples of behavior control and fate control situations A complete and practical prisoner's dilemma game payoff matrix Motivational determinants of each choice in a prisoner's dilemma game Pruitt's l967 decomposed and matrix games The two person, four choice payoff matrix in general form The four choice payoff matrix The six choice payoff matrix The two choice matrix that was used in the study The two choice matrix that was used during the instruction phase of the six choice session The analysis of variance on the probability of cooperation over trial blocks for the EA, CT, SX, OD, and MT factors The analysis of variance for the variance over trial blocks The means and simple effects analysis for the pro- portion of cooperation responses in the sex by contingent interaction for the accommodative strategy The means for the exploitativeness by contingency by sex interaction for the two alternative matrix on the last 25 trials PAGE IO IS 34 36 39 Al 65 67 73 77 82 33 TABLE IS l6 I7 l8 I9 20 2I 22 23 2t. 25 26 27 28A vi The means and simple effects analysis for the sex by blocks interaction The paired comparisons analysis between blocks for the percent c00peration for males The mean variances and simple effects analysis for the sex by trial blocks interaction for the exploitative strategy The paired comparisons analysis for trial blocks for males and females for the exploitative strategy The means and simple effects analysis on the variance of responses for the sex by contingency interaction for the accommodative strategy The simple effects analysis and the mean proportion of MD responses for the sex by contingency interaction Summary table for the sex by contingency by exploitativeness by alternative interaction for trial block four on the pr0portion of each response and the minimum difference necessary for significance The means for the probability of cooperation for the exploitative-accommodative by blocks interaction and the simple effects test The mean variance and simple effects analysis for the exploitativeness by blocks interaction Paired comparisons of variance for the four blocks of trials for the exploitative strategy The simple effects analysis of the contingency by trial blocks interaction Paired comparisons analysis of the proportion of cooperative responses for trial blocks for the noncontingent strategy The means and simple effects analysis of the probability of choosing cooperatively for the accommodative strategy for the contingency by trial blocks interaction Paired comparisons for the contingent accommodative strategy for the probability of choosing cooperatively over blocks PAGE 85 86 88 89 90 9] 92 97 99 100 IOl l03 10A l05 TABLE 288 29 30 3I DI DZ 03 DA 05 D6 D7 DB 09 El E2 vii Paired comparisons for the noncontingent accommodative strategy for the probability of choosing cooperatively over blocks The mean variance and simple effects for the exploitative by contingent interaction The means and simple effects analysis for the contingency by matrix interaction for the exploitative strategy The means for the variance of choices and simple effects analysis for the contingency by matrix interaction The analysis of variance on the first trial choices on the probability of cooperation The probability of cooperative choice for the contingency by matrix interaction The analysis of simple effects for the first trial choice of the two choice matrix The simple effects analysis of the first trial choice of the six alternative matrix The first trial analysis for the maximizing differences alternative The probability of choosing the maximize differences alternative on the first trial for the session by exploitativeness interaction The analysis of variance on the responsiveness scale The analysis of the exploitative-accommodative scale The means for the main effects for the exploitative- accommodative and responsive-unresponsive scales The paired comparisons tests on the probability of cooperation over blocks of trials The mean variance for each block of trials for the contingent and noncontingent strategy for the accommodative strategy PAGE 105 lO7 108 IlO I47 ISO 151 I52 ISA l55 157 l58 I59 165 I67 .‘r-C TABLE E3 E4 ES E6 E7 viii The probabilities of choosing alternative ”A” for the sex by session by blocks interaction The means and simple effects analysis for choosing the ”A” alternative for the EA X CT X blocks interaction The means for the sex by blocks interaction for the vindictive alternative The mean probability of choosing the ”V” alternative for the exploitative by contingency by blocks interaction Means and simple effects for proportion of LR responses for the exploitative by contingency by blocks interaction PAGE I69 I7I I72 I7A I76 FIGURE I LIST OF FIGURES The experimental setting was separated into the above seven rooms Typical experimental room, with the slide projector, screen, response box, and subject position labeled Display of the design of the study with number of subjects in parentheses Drawing of the response box used in the study The viewing screen used in the study PAGE SI 52 SA 59 6I INTRODUCTION The bases upon which people make their day to day decisions, in general, are not available to the researcher of decision making. This situation is most evident in the political arena where few public officials candidly discuss their reasons for choosing a particular course of action. Because the basis of most decisions is hidden from the researcher, it has been necessary to bring the decision making process into the laboratory. A great deal of the laboratory research on decision making has em- ployed a situation which commonly has been called a game. One of the most consistent findings in these game situations has been the differ- ence between males and females in the types of decisions made. Although results that indicate sex differences are frequently obtained, the forms that these differences take are often puzzling and inconsistent. How- ever, attempts to unravel this puzzle can best be dealt with in terms of two distinct theoretical frameworks. These two frameworks are the game theory of Luce and Raiffa (I957) and the social interaction theory of Thibaut and Kelley (l967). Game theory focuses on the utilities of out- comes to the participants in decision making situations, while the theory of Thibaut and Kelley focuses on the interaction between the participants within the context of these utilities. The game theory ap- proach is primarily concerned with individual choice in single decision situations, while the interaction theory is primarily concerned with the sequence of decisions made over many decision points and the effect I of previous choices on the decision process. Theoretical Approaches Game Theory The major impetus for the use of the laboratory in the study of decision making in game theory by Von Neumann and Morgenstern (I947) and by Luce and Raiffa (I957). Particularly it was the work of Luce and Raiffa that demonstrated clearly the usefulness of mathematical game theory in the empirical study of decision making. Luce and Raiffa's theory of games involves the concepts of con- flict of interest and partial control over one's own outcomes. These concepts are the integral part of many interpersonal situations which, therefore, can be viewed as ”games.” This theory of games is based on three assumptions: I) that each outcome has a certain utility for each participant; 2) the utility of each outcome for each participant is known by all participants; and, 3) the participants in the situation are rational. These assumptions define a situation in which each participant knows the outcomes for each decision he might make and he prefers the outcome which has the highest utility. This means that the externally defined outcomes are related to the (internal) utilities. One of the most useful concepts presented by Luce and Raiffa was that of the normal form of the game. This manner of presenting the structure of the game defines the outcome to each participant for each of the possible combinations of choices. The normal form of the game is produced by assuming that each participant has a set of strategies. These strategies are defined as rules which determine the entire sequence of decisions that each of the participants would make during the game. The participants, instead of being presented with a choice of one move or another within the context of the game, are given a choice of all of their possible strategies. From this concept, Luce and Raiffa reduce games of many moves and decision points into a single move, in which all of the participants choose one of their strategies. These combinations of strategy selections define how the game is played and define the outcomes for each of the participants. To present a game in normal form it is necessary that: l) the participants do not know the strategy choices of the other participants; and, 2) the outcome for each participant for each combination of choices is defined and known to the participants. One of the simplest situations that the normal form can represent is that of a two participant game. Each combination of simultaneous choices by the pair results in particu- lar outcomes for each participant and these outcomes have a utility to each participant. Through the normal form of the game a matrix can be constructed with participant one's possible choices defining the columns and participant two's possible choices defining the rows of the matrix. Within each cell of the matrix are the outcomes to each participant for the combination of choices defined by the column and row. This particular representation of a game is called the payoff matrix. The normal form of the game thus makes clear the dependence that each participant's outcomes have on his own choices and those of the other participant. The normal form of the game also offers a framework within which to evaluate the degree to which participants are in a conflict of interest. One way to determine the degree of conflict of interest is to rank order the combinations of choices for each participant in terms of their utility. For the two person situation this means two such orderings will be generated, one for each participant. These orderings of combina- tions of choices are called preference orderings. A conflict of inter- est exists to the extent that the preference orderings differ. The highest degree of conflict of interest is the situation in which the preference orderings are completely reversed; conversely, no conflict of interest exists whenever the most preferred combination is the same for both participants. Since decision making in interpersonal situations is a very com- plex process, most studies of it have been limited to examinations of two person interactions. However, even with just two participants, the the decision making process is still too complex to study effectively if each person has a large number of choices. One approach to the prob- lem has been to reduce the number of choices to two. Thus the basic situation with which game theory has been concerned is that of a two person, two choice situation. Table I displays the general two person, two choice situation. Matrix l in this table presents the symbols designating the four combinations of choices, with each symbol composed of a two letter combination (A and/or B). The first letter in the sym- bol represents the choice of participant one and the second letter the choice of participant two. Matrix 2 in Table I presents the general payoffs for the two participants. Each payoff is also symbolized by a two letter combination (a and/or b) with the first letter representing the choice of the participant receiving the payoff and the second letter the choice of the other participant. A two person, two choice game results in a payoff matrix with four cells. A particular class of games defined by these two by two payoff matrices has been called mixed motive games. These games are Table l. The general two person, two choice situation. Matrix I: Cell designations Participant l A B A AA BA Participant 2 B AB BB Matrix 2: Payoff designations Participant l aa ba aa ab Participant 2 ab bb ba bb characterized by two conflicting motives: The motive to cooperate and the motive to compete. These conflicting motives are apparent in the preference orderings of the outcomes for each participant for the four cells. The preference orderings show the competitive aspect of the game in that the most preferred outcome for one participant is one of the less preferred outcomes for the other participant. The cooperative aspect of the game is derived from the convergence of the preference orderings with respect to intermediate outcomes. The mixed motive game which has been used primarily in the research on decision making has been the prisoner's dilemma game. This game is defined by the preference orderings of the payoffs in the matrix. For a prisoner's dilemma to exist, each participant must prefer the payoffs in the order ba, aa, bb, ab. This means that participant one prefers the cells in the order of BA, AA, BB, AB, while participant two prefers the cells in the order of AB, AA, BB, BA. A prisoner's dilemma also exists if the preference orderings for both participants are reversed. An added requirement is needed if the game is to be played for many trials. If a prisoner's dilemma is to exist over many trials the fol- lowing restrictions also must hold Zaa > ab + ba > 2bb. As the prefer- ence orderings indicate, the most preferred combination of choices for each participant is the least preferred combination of the other. The second most preferred combination for both participants is the AA cell. Another concept that game theorists have introduced, which is of use in the exploration of sex differences, is that of a strategy. Strategies have been defined as complete specifications of what choice to make in any situation. Game theorists have traditionally used the concept of strategy to reduce many move games to a single move. This move then consisted of multiple alternatives where each alternative was a specific strategy. Throughout the remainder of this paper, however, the term strategy is used In a slightly different manner. When sub- jects must choose between the same set of alternatives (strategies) many times, the rules by which they make their choices are also called a strategy in the present discussion. In a sense, these rules consti- tute a super strategy that governs the selection of strategies (as defined traditionally). In the prisoner's dilemma game participants may enter the situa- tion with different goals and the manner in which they go about reach- ing their goals is their strategy. It is the concept of strategy that allows the investigation of game playing behavior in more complex and theoretical terms. Motives generally are not accessible directly, since participants typically are not aware of the reasons underlying their behavior or, if aware of the reasons, they cannot articulate them very well. While their motives are not observable, their choices are, and from these choices their strategies can be inferred. Game theory, however, offers only normative solutions to games: it is the partici- pants who offer the practical solutions of cooperation or defection within the interactive process of the game. Behavior Theo[y_ While the game theorists have developed an extensive theory of how games should be played, based on the utilities involved for a single decision game, they seldom have addressed themselves to the behavioral aspects of repeated plays of the same game. In general, they have treated the situation as a single decision for one individual, an ap- proach which ignores the interaction between participants in a repeated game 5 each F and CI the P' ences maIes repeat interp the ga choice were p TI is the since, tions 0 Thibaut PaFtICII activiti and to s dilemma Mflow. EacI IWeen two '0' the c. is dafinec HIthin the game situation, where previous decisions were likely to have affected each participant's decision on subsequent plays of the game. Rapoport and Chammah (l965) have pointed out this aspect of choice behavior in the prisoner's dilemma game during their discussion of the sex differ- ences which they found in their study. They found that males and fe- males did not differ in their choices on the first few trials of a repeated prisoner's dilemma game but did so after 200 trials. They interpreted this finding to mean that males and females did not enter the game with different tendencies to make the cooperative or defect choices, but that in the process of playing the game the differences were produced. Thibaut and Kelley (I959) have formulated the behavior theory that is the most relevant to decision making in interpersonal situations since, like game theory, it uses a payoff matrix to describe combina- tions of behaviors for the various participants in a relationship. Thibaut and Kelley define matrices within which the utility to each participant in the relationship is presented for each combination of activities in which the group may engage. To simplify the discussion and to show the applicability of their theory to the prisoner's dilemma game only a two choice, two person relationship is outlined below. Each of the two participants in the relationship has a choice be- tween two behaviors. There is a payoff or gain for each participant for the combined activities chosen. Thus, a two by two payoff matrix is defined over the two possible behaviors for each of the participants. Within these dyadic relationships, these matrices of utilities have been defined by Thibaut and Kelley as possessing particular qualities. Two matrix forms of particular interest are those which involve what Thibaut and Kelley have called behavior control and fate control. A matrix In which participant A has behavior control over partici- pant B is presented in matrix I, Table 2. Participant A is able to in- duce participant B to choose the behavior that A prefers. In matrix I, presented in Table 2, participant A prefers that participant B chooses behavior 32, so that A can choose Al which gives him his highest payoff in the matrix. Participant A is able to induce participant B to choose 82 by choosing Al, since B will receive a payoff of A if he chooses 82 and he receives a payoff of I if he choosesEH . This type of matrix al- lows participant A to receive his highest payoff because B receives very low payoffs for not choosing A's most preferred cell. An example of fate control is presented in matrix 2, Table I. In this type of matrix, participant A determines B's gains by his own choice. If participant A chooses Al, he guarantees that participant B will receive a payoff of A while if A chooses A2, he guarantees that B will receive a payoff of l. Participant B has no control over his own payoffs; they are completely determined by participantrA's choice. In this situation, B has no preference between his choices since his pay- offs are only determined by A's choice. Participant A, however, can give B a reason for preferring one behavior over another by responding on the next trial to one behavior by giving B a payoff of A and re- sponding to the other behavior by giving B a payoff of l. Participant A in effect can reward and punish B for his choices. It is in this way that fate control can be converted to behavior control. The crucial difference between behavior control and fate control employed as behavior control is that in the former, participant B IO Table 2. Examples of behavior control and fate control situations. Matrix 1: Behavior control Person A Al A2 Bl I A Person B 82 A I Matrix 2: Fate control Person A Al A2 Bl A I Person B 82 A I II punishes himself on that trial for not choosing the behavior that A desires, while in the latter situation, participant B can only be pun- ished on the next trial for not choosing correctly In an earlier trial. This approach to decision making situations takes on particular significance when considering the prisoner's dilemma game. In this game, the payoff matrix is of the form presented In matrix I, Table 3. In matrix 2 of this table, the payoffs to participant B are presented to emphasize the fate control aspects of the situation. In terms of matrix 2 in Table 3 this means that if participant B chooses to co- operate, he receives A if A c00perates and 0 if A defects and if B chooses to defect, he receives 6 if A cooperates and 2 if A defects. Whether participant B cooperates or defects, he will receive a worse outcome if A defects than if A cooperates. This shows that each player, by choosing to defect, can guarantee that the other participant will re- ceive the lowest outcome for whatever choice he makes. This is a condi- tion of mutual fate control. Application of the Theories to the Prisoner's Dilemma The two theoretical approaches presented above, while both employ- ing the payoff matrix, focus on two different aspects of decision making. Game theory focuses on the payoff matrix and rational behavior with re- spect to the payoffs in that matrix. The theory of Thibaut and Kelley focuses on the behavioral aspects of the decision making situation with- in the context of the payoff matrix. Each of the above theories suggests a different approach to the study of choice behavior in the laboratory. Game theory suggests an approach that focuses on the payoffs to the chooser and the other participant in a single decision situation. The theory of Thibaut and I2 Table 3. A complete and partial prisoner's dilemma game payoff matrix. Matrix I: Complete payoff matrix Participant A Participant B Matrix 2: Participant B's payoff only I3 Kelley focuses on the process involved in making repeated decisions and thus directs research toward the mechanisms of decision making. Payoff Matrix Characteristics Within a payoff matrix, there are three aspects to the payoffs for any choice that is made: I) the payoffs to the chooser; 2) the payoffs to the other participant; and, 3) the relationship between these two payoffs. Whichever choice is made implies particular motivations to the chooser depending on the three aspects of the payoffs for that choice. The “cooperate” alternative in the prisoner's dilemma game gives the chooser either his worst or second best outcome. This alternative also gives the other participant the best outcome that he can receive, no matter his own choice, and it also guarantees that the other participant will do at least as well as the chooser. These outcomes suggest only one motivational determinant, that of maximizing joint gain. By choos- ing cooperatively both players combined will do better than they would if one or both chose the ”defect” alternative. As Opposed to the ”cooperate” alternative the ”defect” alternative suggests many motivations for its choice. The “defect” alternative in the prisoner's dilemma results in the following outcomes: l) the chooser avoids his maximum loss and gains more despite what the other chooses; 2) the other participant is guaranteed his worst outcome despite what he chooses; and, 3) the chooser is guaranteed as much or more than the other participant. The first outcome suggests a motive to maximize own absolute gain. By choosing to defect the chooser is guaranteed a better outcome, despite what the other chooses, than if he had chosen to cooperate. The second motivational determinant of the defect choice, suggested IA by the outcomes of that alternative, could be called vindictive. This choice guarantees that the other participant will receive less despite his choice than if the chooser had chosen to cooperate. Bixenstine and Wilson (I963) have indicated just such a motive may have been salient for some of their subjects. In their study, females were more coopera- tive than males but punished any nonc00peration by the other partici- pant. The third motivational determinant is that of maximizing differ- ences because the chooser is guaranteed at least as large a payoff as the other. Minas, Scodel, Marlowe, and Rawson (I960) indicated that this motivation was employed by their subjects in a two person non- zero-sum game. Table A presents a summary of the motivational determinants for each of the choices in the prisoner's dilemma game. It must be empha- sized that these motivational determinants apply only to single choice games in which repeated choices by the other will not affect the choices made. In games of repeated choices the interaction between the partici- pants affect the choices made. It is assumed that all subjects entering a prisoner's dilemma game play the game with a particular motivation, whether this motivation is to maximize absolute gain, relative gain, joint gain, or to minimize loss. If the other participant in a prisoner's dilemma game always chooses cooperatively or always chooses competitively, the subject would be able to choose that alternative which will best satisfy his particu- lar goal. If the other participant does not choose one alternative lOO% of the time, the subject is faced with the problem of satisfying his desires when he does not know with certainty what the other will choose l5 Table A. Motivational determinants of each choice in a prisoner's dilemma game. Maximize joint gain Maximize absolute gain Maximize relative gain Minimize other's payoffs (vindictive) I6 on the next trial of the game. It is in the response to this non-100% choice of the other that sex differences tend to emerge. Following is a theory that addresses itself to the problem of repeated interactions in a many choice game. Mechanisms of Decision Making Vinacke's Original Theory. The theory to be presented was originally developed by Edgar Vinacke in several different studies (Bond and Vinacke, l960; Uesugi and Vinacke, I963; Vinacke and Gullicksen, l96A; Vinacke, Lichtman, and Cherulnik, I967; and Vinacke and Arkoff, l959) of coalition games. Vinacke asserts that males are exploitative in their goal seeking behavior because they try to maximize absolute gain at any cost to the other participant. Females, on the other hand, are accommo- dative since they try to give an equal payoff to all participants. Fe- males attempt to maximize their gain, but they do so within a prescribed set of behaviors. Although this theory appears adequate for the results from coalition studies, it has been less predictive of the results from the prisoner's dilemma studies. This theory would predict that females would be more cooperative than males in a prisoner's dilemma game; how- ever, several studies have found females to be more competitive than males. In response to this contrary evidence Vinacke (I969) revised his theory. Vinacke claimed that females were accommodating to the experi- menter because they perceived that the experimenter wanted them to com- pete and thus did so. This revision is no more tenable than the orig- inal version, since several studies also have shown that females are more cooperative than males (Tedeschi, Bonoma, and Novinson, I970; Schlemker, Bonoma, Tedeschi, and Pivnik, 1970; and Komorita, 1965). I7 It is the study by Komorita that most clearly refutes the revi- sion. Komorita found that females cooperated more than males when playing against a simulated opponent who cooperated on a 50% or 75% random basis. Males, on the other hand, cooperated more than fe- males when playing against a simulated opponent who responded with the subject's last choice. It is not at all clear why the demand charac- teristics of competition should be more evident to the females in one situation than in the other. This is particularly puzzling considering that the percent of cooperation by the simulated other participant in the 50% random cooperate and the contingent conditions was essentially the same. Revised Exploitative-Accommodative Theory, A possibly more realistic revision of this theory consists of the following premises. Males and females enter the situation with different goals; males try to maximize absolute gain while females try to maximize social welfare (joint gain) and to make an equal division of the payoff. When males and females are confronted with an opponent who does not c00perate or defect l00% of the time, they are both frustrated in their respective goal strivings. Males, in response to this frustration of their goal, attempt to convert their fate control over their opponent into behavior control. This con- version is essentially bargaining with the other participant by indi- cating that the subject will compete if the other competes and he will cooperate if the other cooperates. Females on the other hand respond to this frustration by trying to withdraw from the situation. In a pris- oner's dilemma game, choosing defect can be considered a form of with- drawal. The defect chooser need not consider the choice of the other participant since he is guaranteed of not receiving his lowest payoff. 18 By choosing defect the other has less control over the chooser's out- comes. Some research that offers evidence for this approach is that of Shomer, Davis, and Kelly (I966). They indicated that males used threat as a means of communication more often than did females, a re- sult which supports the position that males bargain after goal frustra- tion. Review of Sex Differences Although many studies have indicated significant differences be- tween males and females, the direction of these differences has not al- ways been the same. In the studies to be reviewed there are some con- sistencies that bear mentioning before the review is presented. In most studies in which males are found to be more cooperative than females, the subjects were playing against a responsive opponent. That is, they were playing against a strategy which was contingent in some manner on what the subject chose. These contingent strategies have been produced either by a simulated opponent playing a strategy which required a particular response for each choice made by the subject or by a real opponent who tended to make responses systematically as a function of the other's behavior. In most of the studies in which females were more cooperative than males, the strategy of the other participant was a noncontingent strat- egy. A noncontingent strategy is characterized by a simulated other who responds according to some preset probability of random choice or with some preset sequence of choices, regardless of the choices of the sub- ject. These results are consistent with the theoretical positions l9 presented previously. The accommodative-exploitative theory predicts these differences since females are frustrated in their attempt to maximize social welfare and thus respond with defection. Males use the situation to bargain with the other participant. In the contingent situation the other participant responds to him and thus the bargaining is successful. If the other is responding to the subject's choices, the subject chooses cooperatively since that is the optimum strategy against a contingent other. The female is less concerned with deter- mining the other's strategy so she chooses as a function of the payoff matrix and the number of times the other has cooperated. In summary: the exploitative-accommodative theory predicts bargaining behavior by the male which, in the contingent situation, leads to cooperation; fe- males in this situation, try to withdraw and are reinforced for this withdrawal by the continued defection of the other participant. Several studies have indicated that females are more cooperative than males. Most of these studies employed a simulated opponent who played a noncontingent strategy. These strategies varied the percent cooperation from the simulated other from 25 - 90%. For those situations in which the simulated other cooperates a high percentage of the time, the accommodative-exploitative theory pre- dicts that both males and females will be able to achieve their respec- tive goals. A high amount of cooperation results in females cooperating to maximize social welfare and to give an equal division of the payoffs. Males in this situation also are able to maximize gain since the simu- lated other cooperates despite the choice made by the subject. In those situations in which percent of cooperation is low, the accommodative-exploitative theory predicts that both males and females 20 will be frustrated. Females trying to maximize social welfare and equal division of payoffs are frustrated by the simulated other who cooperates on only 50% or fewer of the trials. This frustration should lead to defeCtion as a withdrawal from the situation. Males also are frustrated by the low level of cooperation. When males try to bargain with the opponent they again are frustrated because the other participant does not respond. This nonresponse by the simulated other forces the males to defect as the only solution to maximizing gain. The following review of the sex differences literature within the prisoner's dilemma game will be separated into three sections: l) males found to cooperate more than females; 2) females found to cooperate more than males; and, 3) conflicting results within the same study. Males Cooperate More than Females Bixenstine, Chambers, and Wilson (I96A) used an asymmetrical pris- oner's dilemma game with males and females playing in same sex pairs against a simulated other who played an 80% matching strategy. This means that the other participant was playing a strategy contingent on the choice of the subject. The subjects were in the powerful position for one series of trials and in the weak position for one series of trials. The results indicated that males were more c00perative than females, and that females were more likely to retaliate to exploitation with defection while males were more tolerant of exploitation and to employ it more often. Since males enter the situation with the motivation to maximize gain they would less resent this strategy in someone else and therefore be more tolerant of it. If females entered the situation with the moti- vation to maximize social welfare, they would be less tolerant of Zl exploitative behavior that frustrated this motive. Thus this study seems to support the exploitative-accommodative approach. Another possibility however, is that males and females were just following their pattern which Is consistent for contingent play and that the researchers inferred a vindictive style on the part of the females. Whichever ap- proach is taken this study alone is not a refutation of the theory pre- sented. A study performed by Bixenstine and O'Reilly (l966) used males and females in same sex pairs with electric shock as well as money as pay- offs. Shock increased cooperative behavior for both sexes but much less so for females. The general findings of this study indicated that fe- males were less trusting and they respond more resentfully, conserva- tively, and competitively than did males. Females also did not under- stand as well as males what the optimum strategy was in the game. This study seems to offer support for the theory in that the authors indicate that females are less understanding of the situation, play a conservative or less risky strategy, and that they respond vindictively and competitively. Oskamp and Perlamn (I965) used males and females in same sex dyads for 30 trials. These subjects were drawn from a small college popula- tion. The results, which indicated that males were more cooperative than females, added support to the theory in that the other two studies were performed at Kent State University, a much larger university. A very interesting study performed by Sampson and Kardush (I965) used children in a summer camp. These subjects played a prisoner's dilemma game for candy during their game period at camp. They competed in same sex dyads with the age of the children, race and socio-economic 22 status of parents used as independent variables. Because of the low frequency of Black children particularly in the high socio-economic category, the analyses performed were on collapsed cells, systematically ignoring certain of the independent variables. The results of this study indicated that for White children there was an interaction between age and sex with respect to percent of cooperation; younger males were less cooperative than older males and younger females were more coopera- tive than older females. Thus, if the accommodative-exploitative dis- tinction is valid, this study seems to indicate an Increasing conformity to appropriate sex roles with increasing age. After the experiment the authors questioned the children to deter- mine the motivation for the choices made. The results of the question- ing were categorized by type of response: I) risk taking; 2) competi- tive; or, 3) polite collaboration. Again a sex interaction appeared. With respect to risk taking, younger females indicated concern 22% of the time while older females were concerned with the risk involved 7I% of the time. Regardless of age males seldom mentioned this aspect of the game. Competitive responses were similar for both sexes but de- creased from younger to older with males decreasing from 32% to 28% and females decreasing from 33% to IA%. The category ”polite collaboration“ again produced a sex by age interaction with males increasing their percent in this category from 26% to A3% with an increase in age while females showed just the Opposite trend in that they decreased from AA% to IA% with an increase in age. This study points out most clearly the relevance of the risk in- volved in the prisoner's dilemma and the differential attention that males and females pay to it. The results of the questioning also seem 23 to be of relevance for the accommodative theory since females seem to be no more interested in the cooperative aspects of the game than were males. This may have been due to the fact that females in the older bracket were l0 and II years old and just entering adolescence. What effect adolescence might have on game playing behavior certainly isn't clear but this negative result is not enough to discount the accommodative-exploitative theory. In all of the above studies males and females have played in same sex dyads with the result that females were found to be more competitive than males. A study which did an extensive analysis of same sex and mixed sex dyads was done by Rapoport and Chammah (I965). In this study males and females played either another male or a female for 200 trials. The subjects actually played the game and no simulated other was em- ployed. The general findings were that female dyads were more competi- tive than male dyads and mixed dyads were between these two. Female dyads started out at nonsignificantly more cooperative than males but showed a decrease in cooperation over the 200 trials. The authors in- dicate that in mixed sex dyads males bring females up in cooperative responding and females bring males down in percent cooperative re- sponding. The authors also indicate that it is the process of playing the game that differentiates between males and females and not any pre- play preferences for one response or another. The differences that did appear did not do so until after trial 50, which seems to indicate some minimum number of trials necessary for the emergence of sex differences in contingent situations. 2A Females Cooperate More than Males In contrast to the studies presented previously there are several studies which indicate that females are more cooperative than males. Aranoff and Tedeschi (I968) used two matrices; one of high and one of low conflict. The subjects played in same sex pairs with females pro- ducing more cooperative-cooperative choices than males in the low con- flict matrix. The subjects were given an original stake and then played the game for 200 trials. The authors claim that sex differences occur only in low conflict situations. The result from this study is at odds with much of the previous research using contingent situations. How- ever, even though the c00perate-cooperate responses differentiated be- tween males and females there was no overall difference in the amount of cooperation. i Schlenker, Bonoma, Tedeschi, and Pivnick (I970) found that in a prisoner's dilemma game a noncontingent 50% coOperative strategy pro- duced more cooperation in females than in males. An interesting inter- action between sex of subject and exploitative behavior by the simulated other was found. The simulated other sent two messages containing threats to the subjects: I) a compellence threat, ”If you do not choose cooperatively on the next trial, I will take I0 points away;” or, 2) a deterrence threat, l'If you choose competitively on the next trial, I will take l0 points away.” After the threat was sent the simulated other was either exploitative or cooperative on the next trial. If the other was exploitative, females had the lowest percent cooperation of all conditions and sexes. Females in the compellence-exploitative con- dition had significantly fewer cooperative choices than females in the other three conditions or males in the compellence condition. 25 The finding that females defect more in an exploitative-compellence condition is quite interesting. In the compellence condition the ex- ploitative behavior is the most obvious since the emphasis is placed on cooperating not competing. This would offer support for the accommodative-exploitative theory since females seem to be responding to the exploitative behavior in a negative way. It does seem that while females choose defect in this situation it may not be a withdrawal choice but a choice to punish the other for his exploitative behavior which fe- males do not accept. The general results of this study offer support for the theory that females were more cooperative in a noncontingent situation than were the males. Tedeschi, Powell, Lindskold, and Gahagan (l969) had males and fe- males in same sex dyads play against a preprogrammed 25% cooperative strategy for IIO trials. This situation was similar to the previous study in that the simulated other could send threats. HoweVer, in this study the subjects were able to reply to this threat with a note that indicated cooperation on the next trial, competition on the next trial or did not indicate what they were going to do. The only sex differ- ences found were that females were more cooperative over the last 20 trials than males and females were more truthful in their responses than were males. In this situation, where the subjects are playing against a noncontingent strategy, the theory predicts that females will cooperate more than males. The fact that this difference does not ap- pear until the Iast 20 trials may be due to the very low percentage of c00perative responses. Tedeschi, Lesnick, and Gahagan (I968) used the same procedure as in the above two studies for l00 trials against a preset 50% cooperative 26 strategy. Females were more c00perative on trials 2, 5, and IO but the differences disappeared by the end of the I00 trials. This finding is at odds with the finding of Komorita (I965) which found that in over 80 trials females were more cooperative than males playing against a strategy which responded to a cooperative choice with cooperation on 50% of the trials. This study again employed note sending and this may have produced the inconsistent result, or it may be that 50% c00perate is too low to produce any sex differences, with males and females both defecting. Tedeschi, Bonoma, and Novinson (I970) used the same experimental design as in the previous studies with the difference that subjects could send threats and impose fines for nonCompliance. If the subjects imposed a fine they could either lose 5 points themselves (fixed cost condition) or the simulated other could retaliate by taking 5 points away. These two conditions were called the fixed cost and retaliation conditions and the study was run for ISO trials. The results indicated an interaction between sex and condition with females sending fewer threats than males in the fixed cost condition but sending almost the same number in the retaliation condition. The percent of cooperation indicated that females were more likely to c00perate in the retaliation condition while males cooperated 85% of the time in the fixed cost condition and 20% of the time in the retaliation condition. There was an overall sex difference with females more cooperative than males. The last study to be presented in this section is that of Tedeschi, Bonoma, and Lindskold (I970). These researchers used the same procedure as the above studies and again found that females were more cooperative after threats and over all. 27 All the studies presented in this section used some form of com- munication and rather low percentage of c00peration by the simulated other. While the results have been to some extent consistent it would certainly seem that both of these factors would tend to mitigate any differences that might be present. The process of sending notes may make the interpersonal aspect of the situation more salient to both males and females but it may affect females more than males. What seems to be a plausible hypothesis is that females only attend to the interpersonal nature of the situation when it becomes apparent and only then do they respond by vindictive behavior. Definitive Studies Three studies have made direct comparisons between the contingent and noncontingent strategies. Komorita (I965) used males and females in an 80 trial prisoner's dilemma game. In the noncontingent situation the probability of cooperation from the simulated other given cooperation by the subject on that trial was varied, using values of .25, .50, and .75 for this probability. Also in the noncontingent situation the probabil- ity of defect by the simulated other given a defection from the subject was varied over the same values. These two factors of three levels each were combined in a factorial design producing nine different combina- tions of cooperation given cooperation and defection given defection. In the contingent situation the simulated other played a tit for tat strategy in which he echoed on trial n the response of the subject on trial n-I. The results of the study showed that females increased cooperation over the values of noncontingent cooperation given coopera- tion while males consistently played a l0% cooperation over all values. In the tit for tat situation the males c00perated more than the females 28 with the probability of cooperation in that situation being .A8 for males and .23 for females. These results add to the evidence presented previously with respect to the contingent-noncontingent dimension. Males cooperate more in a contingent situation while females cooperate more in a noncontingent situation. There are some problems in interpreting Komorita's results due to the design used in the study. Each level of probability of cooperation given cooperation was combined with each level of defect given defec- tion. These combinations meant that the subjects in some conditions received inconsistent information. An example of this inconsistency is the situation in which the other participant responded to coopera- tion with cooperation on 25% of the trials and responded to defection with cooperation on 50% of the trials. This, in effect, appeared as a contingent strategy to the subject since the other responded differen- tially to cooperation and defection. This confusion causes problems for the direct comparison of contingent versus noncontingent strategies. In an attempt to solve some of the problems of the Komorita study and to make a more accurate comparison between contingent and noncon- tingent situations O'Grady (I970) performed a study using males and females in a 90% noncontingent c00perate or a 90% tit for tat condition. Again males cooperated more than females in the contingent situation and females cooperated more than males in the noncontingent situation. An interesting result of this study was that females in the contingent situation cooperated less than the females in the noncontingent situa- tion and males in the contingent situation cooperated more than males in the noncontingent situation. This result indicates that males and females are responding differentially to each condition and that the 29 previously found interaction between sex and strategy was not due to differential responding by one sex or the other. Kahn, Hottes, and Davis (l97l) also varied the contingency of re- sponse. They found'both males and females were more cooperative with a contingent strategy than with a noncontingent strategy. A trial by strategy by sex Interaction did appear. Males in the contingent situa- tion increased cooperation over trials while males in the noncontingent situation did not. Females in the noncontingent situation decreased cooperation over trials while females in the contingent situation did not. On the later trials in the game males discriminated between con- tingent and noncontingent strategies while females did not. However, on a questionnaire males and females showed no differences in understanding contingent versus noncontingent play.. One of the most extensive studies with mixed-motive games was per- formed by Sermat (I967). Four separate experiments were performed with males and females. Three of these studies followed the same format and design: thirty trials of l00% noncontingent choices were followed by a trial on which the other either cooperated or defected and then this was followed by 200 trials of tit for tat choices by the simulated other. Experiment I indicated no sex differences. Experiment 2, however, indicated that males who received 30 trials of competition were more cooperative than any other sex or condition while females who received the competitive 30 trials were half as cooperative as the females who had received the cooperative 30 trial pretreatment. A very interesting re- sult of the pretreatment was that both sexes exploited the other partici- pant. It was indicated to the subjects that the other participant would not know which choice they had made so the anonymity of the situation may 30 have caused this effect. Despite the cause, the fact that females ex- ploited the other, .23, chose competitively in the I00% c00perative j_ situation, is a very interesting result and seems contrary to most of the previous results presented. Experiments 3 and A were designed to test differences between the prisoner's dilemma game and a chicken game. In the fourth experiment the simulated other played a tit for tat strategy over all 232 trials while eXperiment 3 followed the same design as eXperiments l and 2. As opposed to the prisoner's dilemma game a competitive strategy by the other produced more cooperation than the prisoner's dilemma game.‘ The reason is rather obvious; in a chicken game playing against a defect strategy the optimum strategy is to cooperate. The interesting aspect is that no sex differences were reported for these situations. All of the studies presented above offer support to the revised exploitative-accommodative theory. As was pointed out earlier, the sex by strategy interaction is predicted by the theory. The results from the Kahn, Hottes, and Davis study indicate that males increase coopera- tion over a contingent situation which is predicted by the accommodative- exploitative theory. In a contingent situation males successfully bar- gain for mutual cooperation. One anomalous result was that females de- creased the amount of cooperation over trials in the noncontingent situa- tion. However, females were shown at the end of the game not to dis- criminate between contingent and noncontingent strategies while males did make the discrimination. The results of the Sermat study with respect to the exploitative be- havior of males and females indicated that females as well as males were willing to exploit the other if he cooperated I00% of the time. 3I The accommodative-exploitative theory, however, predicts that fe- males would cooperate more with a l00% cooperative strategy because this maximizes social welfare as well as equalizes payoffs. This Is not con- clusive evidence against the exploitative-accommodative theory since the game was played for only 30 trials and the differences between males and females may not have had time to develop. There certainly are prob- Iems of subject suspicion with a I00% cooperative strategy. Sermat does not address himself to this problem which leaves one to wonder about the validity of the data. ‘ No Sex Differences Found Several studies have reported no sex differences in the mixed- motive game. Of these studies a few have involved less than 50 trials. Lutzker (I96l) used a chicken game with mixed sex and same sex dyads for 30 trials and found no differences. Kanouse and Wiest (I967) found no differences in one trial paper and pencil prisoner's dilemma. Komorita and Mechling (l965) had males and females play against a simu- lated other. The experiment was only terminated after the subject had responded with five consecutive cooperative responses following a de- fection. The largest mean number of trials for any condition was 30. The final study using less than 50 trials was performed by Miller (I967) and again no sex differences were found. These results lend support to the finding by Rapoport and Chammah (I965) that sex differences do not emerge until later trials. Bixenstine, Potash, and Kellogg (I963) conducted a study in which the first 30 trials were 83% random cooperation or 83% random defection, after which there were 60 trials of 83% matching. The results for the last 60 trials were the same as for the first 30; no differences between 32 the sexes in the percent of cooperation. Also no differences were found between the 83% random cooperation and the 83% random defection. The results of the Rapoport and Chammah study again come to bear. These authors have indicated that at least 60 trials are necessary for any sex differences to appear. The intrusion of the 60 trials of con- tingent strategy may have suppressed any sex differences that were about to emerge. The conflicting sex differences may have cancelled each other out. Hurst (l969) used males and females in a mixed-motive game after they had been given drugs. The author reported no sex differences but he had only a few females in the study. Despite the small number of females the author indicated that females approached the game in a c00perative spirit but responded to defection strongly. Again this is an inference about the motivation for choosing the defect alternative. A rather interesting study was performed by Evans and Crumbaugh (I966) in which males and females played a prisoner's dilemma in same sex dyads. They played a nonmatrix form of the game for IOO trials and no significant differences were found. It might be that the nonmatrix form of the game eliminates any sex differences. The exact reason for this is not immediately obvious. Horai and Tedeschi (I969) had males and females play a simulated other for ISO trials with a 50% random cooperation strategy. The SA trials on which threats were sent to the subject to coerce him into cooperation were always defection trials. No difference was found in this situation In percent cooperation but they did find that males lied significantly more often when replying to the threat than did females. The authors explain the difference in terms of the relevance of the game [I M. gh- playing S't' males. The that the sel and the ver' Pruitt forms of a c These four g between male prising cons form resulte vious soluti readily expl. of sex diffe Situations m.- 29: From th' theory adeque Seems that me f°r Particule aspects to ti‘ the Choice to There a r PTObIem. one discriminate the four mOEI‘ ilvationa) de 33 playing situation for the male role and the relative irrelevance for fe- males. The reason for the lack of difference between the sexes may be that the sending and receiving of notes in some way alters the situation and the very low percent cooperation by the other. Pruitt (I967) used males and females in same sex dyads playing three forms of a decomposem‘prisoner's dilemma and one matrix form of the game. These four games can be seen In Table 5. Pruitt reports no differences between males and females in this study. This result is extremely sur- prising considering the payoffs in form I of the decomposed game. This form resulted in the least amount of cooperation despite the rather ob- vious solution of A for both males and females. These results are not readily explainable; however, the large amount of evidence in support of sex differences indicates that the absence of differences In these situations may be due to the procedure used rather than real. Definition of Problem and A Proposed Solution From this review, it is clear that the accommodative-exploitative theory adequately accounts for the prisoner's dilemma data. Also it seems that males and females may be choosing the ”defect“ alternative for particular characteristics of the payoff matrix. Thus there are two aspects to the problem: I) what aSpects of the payoff matrix Influence the choice to defect; and, 2) can the theory withstand a rigorous test. There are at least two approaches to the solution of the first problem. One approach is to construct various two by two matrices which discriminate between the various motives for choosing the ”defect” alter- native and a second is to construct a matrix which differentiates between the four motivations within the matrix. Because at least two of the mo- tivatlonal determinants depend on reactions to a defect choice, two 3A Table 5. Pruitt's l967 decomposed and matrix games. Your Other's Gains Gains C 6 6 0 I2 -6 Your Other's Gains Gains C 0 I2 D 6 0 Your Other's Gains Gains c -6 18 D O 6 C 0 l2 l8 C l2 0 O 6 D 18 6 3S choice matrices are not a feasible solution to the problem. Payoff Matrix Because males and females may be using the same strategy choice for different reasons in different situations, two eXpanded payoff matrices have been designed. Although several researchers have used matrices with more than two choices (Pillsuk, Potter, Rapoport, and Winter, I965; and Gallo, Funk, and Levine, I969) the present matrices differ from those in that they are not progressions of more extreme prisoner's dilemmas. The present matrices involve several types of games and strategies. AxA Payoff Matrix. The first payoff matrix to be presented separates the three motivations for choosing to defect and the one motivation for choosing cooperatively in the prisoner's dilemma game. Table 6 presents the AxA payoff matrix with symbols for the payoffs. Each payoff of the matrix is represented by a two letter combination. The first letter in the combination corresponds to the choice made by the participant re- ceiving the payoff while the second letter corresponds to the choice made by the other. The ai's represent the payoffs for choosing maximum absolute gain where the i's represent the choice of the other (a, v, c, or d). The vi's represent the payoff for choosing vindictively while dI represents payoffs for choosing to maximize relative gain and ci, the payoffs for choosing cooperatively. ”Maximizing absolute gain” is defined as receiving the greatest payoff for that choice despite what the other participant chooses. This means that the parameter al must be larger than any other parameter for a given choice of the other or ai > xi where x - (v, c, d) and l - (a, v, c, d). Cooperation is defined as maximizing joint gain or social welfare 36 Table 6. The two person, four choice payoff matrix in general form. A V C 0 aa va ca da A aa av ac ad av vv cv dv V va vv vc vd ac vc cc dc C ca cv cv cd ad vd cd dd 0 da dv dc dd A = maximize absolute gain < I vindictive-~minimize other's gain C - cOOperate--maximlze joint gain 0 I maximize difference (relative gain) and is 0P‘ participa! payoffs TI symbols, 1 and d. The n having the other payc rameters t connote gi' another re: be lower tI' the other p and d). "Maxim For this ch Participant Y' ' XI, whe Participants Pant chooses These f. ters o,- Payoi ”equalities “strum” i 'W Payoffs a than CI Shoui aHdi >ci 37 and is operationalized by having the sum of the payoffs for the two participants for the cooperative choice be greater than the sum of the payoffs for the two participants for any other choice. In terms of the symbols, this means that ci + xc > xj + yi, where I, j, x, y - a, v, c, and d. The minimizing of other's gain (vindictive) is operationalized by having the payoff to the other for any choice he makes smaller than any other payoff for any other choice of the chooser. In terms of the pa- rameters this means that xv < xl. Also since vindictiveness seems to connote giving the other his worst despite what it does to the chooser, another restriction on the parameters Is that the chooser's payoff must be lower than for any other choice he might make despite the choice of the other participant. This means that vi < xi with x, I - (a, v, c, and d). "Maximizing relative gain” is really “maximizing differences.“ For this choice the chooser must do at least as well as the other participant. In terms of the parameters this means that di - xd > yi - xj, where x, y, j, i - (a, v, c, d). The difference between the participants is greater for this choice despite what the other partici- pant chooses than for any other choice that he may make. These four inequalities put restrictions on the size of the parame- ters or payoffs. From these equations alone the following two general Inequalities hold: ai > di, cl > vi; and, xcr> xa > xd > xv. If the restriction Is made that cooperation should be a choice in which very low payoffs are obtained if the other does not also choose cooperatively than cl should be less than di. This changes the first Inequality to al > di > ci > vi. Although these equations do specify very particular ranges parame vc and AxA Pa Table T six di the ch: definii can be ings gi specifi Prefere game, a althoug 6x6 PaZ' the thri there a, defect C males pl invoIVed and Novi. crane”; haV'OF cc ‘WehaVIOr wiu'tWOj tiVeneSSu 38 ranges, they do not specify completely all of the relationships between parameters. For example, it does not specify the relationship between vc and aa and this decision is arbitrary. From these inequalities, a AxA payoff matrix was developed. This payoff matrix is presented in Table 7. These four choices, when combined in two choice matrices, produce six different games. Table l, matrix 2 presents a general 2x2 game with the choices being A or B and the payoffs aa, ab, ba, and bb. Given the definitions of the motivational determinants of choices these payoffs can be formed into preference orderings. Five of the preference order- ings give strict inequalities for the four payoffs while the sixth only specifies that aa and ba are greater than ab and bb. The five complete preference orderings include one chicken game, one prisoner's dilemma game, and three games in which vindictiveness is one of the motivations although vindictiveness was not always one of the original motivations. 6x6 Payoff Matrix. Although these four motivational determinants specify the three different motives for choosing defect on a one trial basis, there are two other determinants that have been mentioned for making the defect choice. Sampson and Kardush (l966) found that ll year old fe- males playing a prisoner's dilemma game indicated a concern for the risk involved while males did not. Several other studies (Tedeschi, Bonoma, and Novinson, I970) have indicated that defect was used to induce coop- eration; that Is, as an attempt to convert limited fate control into be- havior control. The two additional motivations are ”minimize risk” and ”behavior control.” These two additional motivations are lntertwined with two previous motivations, "maximizing absolute gain” and ”vindic- tiveness” respectively. SSOIOHD SIMSHlO 39 Table 7. The four choice payoff matrix. YOUR CHOICES I 2 /I I 6 I -3 3 m 5 9‘ '6 It. -1 lloli. In. lllh. -1. L, Ell. ||.I —-u: N N I? l __\o P‘- f9 4% IIL I _ --\n :5... I N. Iii iii“... III... ‘44}; " " iu'I‘ A0 “Minimizing risk” is also “maximizing absolute gain” since the least risk is taken by choosing an alternative that gives the highest payoff despite what the other chooses. To solve this problem, the “maximize absolute gain” alternative was split into two separate alter- natives. Table 8 presents the 6x6 payoff matrix. Both alternatives give greater payoffs than any other alternative despite the choice of the other participant. The relationship between the alternatives is such that each gives a greater payoff than the other for two of the choices the other participant could make and for the two remaining choices, the mean payoffs for the two alternatives are equal. The dif- ference between the two alternatives is that the ”maximizing absolute gain“ has a much larger variance between the payoffs than does the ”minimizing risk” alternative. To eliminate any effect of payoffs, the mean payoff to the other participant for the two alternatives has the same mean value and approximately equal variances. The second new motivational determinant is that of communicating with the other participant by punishing noncooperation. This is an at- tempt to use fate control as behavior control. The new alternative has all of the aspects of vindictiveness except that it gives a high payoff for cooperation and'low payoffs for any other choice. All of the other payoffs are identical to the “vindictive” payoffs. Although two more alternatives have been added there is not an Increased number of 2x2 games because of the duplication of some of the 2x2 games from the AxA. This is so because each of the added alternatives has all of the char- acteristics of one of the alternatives in the AxA matrix. The matrix presented in Table 8 is the 6x6 matrix that will be used in the study. Choice “I” (A) is the “maximizing absolute gain“ SBOIOHO SuUiHlO AI Table 8. The six choice payoff matrix. YOUR CHOICES I 2 3 A 5 6 6 \. -3 3 ‘ 5 6 6' -I 22 2 6 I ll .. ‘ -I0 \ -9 A 4+ I 2 -IO to -9 -2 IJI__, L __ _ I0 \ 13 A IA is IO -9 I3 -6 2 7‘ II _ .. \ ~9 \ -6 -3 3 -9 I . -A' M -3 A i-li _ I" h L -2 2 \ A 6 -2 h] I5 3 6 2! |.k ; A I -Io 7 4. 2 Ino -IO l0 -9 -2' 40' ill _ Ii A2 alternative since the chooser gains more than he does for any other choice except if the other participant chooses alternative ”2“ or alternative “6.” If the other chooses either of these alternatives, the subject receives very low payoffs. The chooser generally receives very high payoffs if the other participant chooses either of the first, third, fourth, or fifth alternatives. He receives very low payoffs if the other chooses either of the ffirst two alternatives. This indicates a high risk situation but offers ihe largest gain. The second choice in this matrix is called the vindictive choice (V) since it guarantees that the other participant will receive his worst payoff for each choice that he may make. While this gives the other participant his lowest payoffs it also incurs losses for the chooser. Only if the other participant chooses alternative ”3“ does the chooser get a positive payoff. The third alternative in the matrix is the c00perative choice (C) since the combined payoff for this choice is greater than the combined payoff for any other choice. If both participants choose cooperatively on every trial, they will each receive more than if they try to maximize absolute or relative gain or if they try to minimize risk. If one participant chooses cooperatively and the other chooses alternative ”I,” ”2,” “A," or ”5," the participant who chose cooperatively will get a very low payoff. . The fourth choice in the matrix is a low risk choice (R) since it avoids the largest loss and has no cell in which the chooser receives a negative payoff. Although all cells give the chooser a positive payoff, these payoffs are rather small compared to the payoffs for choice ”I.” The standard deviation between the payoffs for this choice Is much less A3 than the standard deviation between the payoffs for choice ”I.” The mean payoff per cell, however, for choice ”3” is equal to the mean pay- off per cell for choice ”I.” This indicates that the third choice in- volves less risk than choice ”I“ while giving the same payoff per cell. Alternative ”5” maximizes differences (0) or relative gain. While the amount won for each choice is less than that won for the maximize absolute gain the difference between the participants In the amount they each receive is greater than for any other choice the chooser could have made. This alternative also presents the chooser with low outcomes if the other participant chooses alternative ”2,” "A,” or ”6.“ While the differences between participants is maximized, the loss incurred by the chooser can be great. Alternative "6'I is called behavior control (B) since the other participant is forced to choose COOperativer if his Opponent chooses B consistently. The other participant receives large negative payoffs for all choices he makes except for cooperation and minimizing risk. The payoff for choosing minimizing risk is much smaller than that for choosing to cOoperate. Summary. This payoff matrix allows the differentiation of the choices of minimizing risk, maximizing absolute gain, vindictiveness, coopera- tion, and maximizing differences. The matrix differentiates the competi- tive choice of the prisoner's dilemma into five different choices which reflect five different motivations for choosing the competitive choice in the prisoner's dilemma game. If males are optimizing gain, they will choose the maximize absolute gain alternative if the other plays noncon- tingently and the cooperative choice if the other plays contingently. Males also may choose behavior control against an opponent who does not AA play cooperatively and plays contingently. For whatever reason females are choosing defect, to minimize risk as the accomodative-exploitative theory predicts or vindictiveness or maximize absolute gain, this matrix should differentiate between these motivations. Test of the TheoLy To test the viability of the revised eXploitative-accommodative These strategies r—fl i t theory, four different strategies were developed. were then employed in a prisoner's dilemma game as well as in the six choice game. Strategies. The strategy of the other participant has a great effect As has been consistently shown, males on the responses of the subject. and females respond differentially to contingent and noncontingent strategies. In the prisoner's dilemma game these strategies are quite well defined. An unconditional strategy is some fixed percent of the trials on which a cooperative choice will be made, with the defect choice made on the remaining trials. 0f the many contingent strategies that could be employed the tit for tat strategy of echoing the choice of the subject on the preceding trial has been used almost exclusively. The "tit for tat" strategy consists of the simulated other partici- pant choosing on trial n the alternative chosen by subject on trial n-l. There have been several modifications of this strategy involving increasing the number of trials between the choice and the echo of the choice, by having the simulated other echo on only a certain percent of the trials. These modifications only serve to confuse the situation since they make the possibility of ascertaining the type of strategy played by the other very difficult. Given a six alternative game there are over 100,000 different AS strategies, where strategy is defined as choosing alternative "x" If the other participant has chosen alternative "a" on the previous trial. However, of the more than lO0,000 strategies only a few are rational in the sense that they areDconsistent. An example of a nonrational strategy is one which responds to maximizing relative gain and vindictiveness by cooperation and responds to the remaining alternatives with vindictive- ness. Of the consistent (though possibly not rational) strategies for a 6x6 matrix only six are unconditional. These strategies are of the form choose alternative x on trial n if the other has chosen a, b, c, d, e, or f on trial n-I. The remainder of the rational strategies consist of some form of contingent strategy, or choose x on trial n if the other has chosen a, b, or c on trial n-I and choose y if he has chosen d, e, or f. Contingency of Strategy. While both the contingent and noncontingent strategies are well defined for the prisoner's dilemma game, they are not nearly so well specified for the six choice game. For the noncon- tingent strategy specifying a certain percent of the trials as coopera- tive does not completely determine the responses to be made on the re- maining trials as it does for the prisoner's dilemma game. In a pris- oner's dilemma game a 90% cooperative strategy determines that defect will be chosen on the other l0% of the trials. in the larger matrices an 85% cooperative strategy leaves the problem of how to respond on the other l5% of the trials. The simplest solution is to divide the re- maining percent of the trials equally between the remaining alternatives. The implementation of the typical "tit for tat" or contingent strategy for a six choice game would certainly cause the subjects to A6 become suspicious. This problem is particularly acute for the six choice game because the behavior control alternative requires a particu- lar remxnme. IAgainst a player who chooses behavior control consistently only Uw>alternatives are rational choices for the simulated opponent: I) COOperatkNu or, 2) low risk. A more realistic class of contingent strategies than tit for tat is indicated by the division of the defect choice. This class of contingent strategies consists of the following five strategies: I) choose I'maximize absolute gain” in response to all choices except cooperation and then cooperate; 2) choose ”vindictiveness” in response to all choices except cooperation and then cooperate; 3) choose ”minimizing risk” in response to all choices except c00peration and then COOperate; A) choose ”maximizing relative gain” for all choices of the other except cooperation and then cooperate; and, 5) choose “behavior control” in response to all choices except COOperation and then These strategies are just forms of the tit for tat simulated cooperate. The strategy re- strategy employed in many of the studies reviewed. sponds to cooperation with cooperation but to defection in its various forms by defection of one form. Contingent and noncontingent strategies Exploitativeness of Strategy. can vary! U1 their degree of COOperation and defection. Given the ex- pected differential responses of males and females to defection and cooperation, two different types of strategies will be developed. These strategies represent two classes of strategies that might be called accommodat ive and exploitative. The type of person characterized by the accommodative theory pre- ented previously implies a strategy of cooperation until the other de- ects for several trials, after which withdrawal from the situation IS A7 attempted. The purpose of the accommodative strategy Is to make the shmnated other appear to be cooperative. The simulated other must appear to be a trusting person interested in the dyad's joint gain. A person playing an exploitative strategy implies a type of person who is interested in his own gain and not interested in what the other person receives. This person is characterized by exploiting any coopera- tion. An exploitative strategy must give the impression of an inconsid- erate, self-interested person. This strategy when confronted with an uncOOperative other will try to bargain with the other participant to induce cooperation. Once the other cooperates, the exploitative strat- egy will exploit again. Hypotheses The four strategies presented (contingent accommodative, noncon- tingent accommodative, contingent exploitative, and noncontingent exploitative) anchor two different dimensions of strategies: I) con- tingent-noncontingent; and, 2) accommodative-exploltatlve. The exploitative-accommodative theory makes particular predictions for the relationship between number of defections of males and females in the prisoner's dilemma game for these four strategies. There also are some predictions as to the effect that each of the strategies has on all subjects. Hypothesis l. Females will defect more than males under contingent strategies while males will defect more under noncontingent strategies.’ Hypothesis 2. Against an exploitative strategy the variance of choices for females should be less than the variance of choices for males during the first several trials. 'These hypotheses follow directly from the exploitative- A8 mmommflafive theory assumptions as to the differential response to fnwtratkm by males and females. The rationale for Hypothesis l was thatnmlesvnll originally try to bargain while females will defect in resmnme Unconditional responding of the other participant. The secondiwpothesis follows from males trying to bargain and thus will vary Uwfir choices to try to get the other participant to choose coopera- Females, however, will not bargain and will simply choose to tively. defect against an eXploitative strategy. In later trials males and fe- males should both be defecting. Against a noncontingent accommodative strategy males should choose the ”maximize absolute gain” alternative while against a contingent strategy females should choose the “minimize risk'I alternative. Hypothesis 3. Against a noncontingent accommodative strategy males should choose to defect while females should choose to cooperate. Hypothesis A. The third hypothesis was derived from males' original motivation to maximize their own gain despite the cost to the other participant, and also from females' response to frustration. Females respond to the frustration cfi'their goals by attempting to leave the situation. The 'hwhwhnize risk” alternative clearly satisfies this desire since the other participant has little ability, in this situation, to affect the payoffs to the chooser of "low risk". TWwe Iksurth hypothesis was also generated by males' desire to maximize gain since against a noncontingent accommodative strategy the alternative which maximizes gain is the defect alternative. Females will cooperate with a noncontingent accommodative strategy since the theory predicts that females try to be fair and divide the‘payoff equally. A9 Thelasttwo hypotheses deal with the general effect of the strategies on all of the subjects regardless of sex. IMpoUufiis 5. There should be more defection under an exploitative strategy than an accommodative strategy. Hypoflwmis 6. There should be more cooperative responses under a contingent strategy than under a noncontingent strategy. METHOD Subjects The subjects who participated in this study were a sample from a larger mxfl of subjects maintained by the Cooperation/Conflict Research Group atIHchigan State University. All of the subjects in the pool were recruited for money to participate in “motivational research.'I The recruitment of subjects took place during the first week of the term and included a newspaper advertisement and personal appeals in each of the introductory psychology classes. Twelve hundred subjects were recruited for the pool and of these, I96 subjects participated in the study. Although I96 subjects participated in the study only I28 were actually used in the analyses. l) A8 subjects indicated they felt they were not playing Sixty-eight subjects had to be discarded: against a real person; 2) A subjects played against someone of a different race; and, 3) machine failure occurred for I6 subjects. m Four 6'x8' rooms served as the experimental rooms. One subject was placed in each of the rooms As the Subjects were isolated from one another. with the door closed. Figure l shows the experimental setting. figure indicates, there were two large rooms directly behind the larger The first of these rooms was used as a storage room and a center room. The second of the rooms housed the noise buffer for the computer. computer that controlled the experiment. Figure 2 shows the layout of the experimental rooms. 50 The subject 5i Hallway Experimental Experimental room F room A EXperimental . Experimental room E room B Storage Room Apparatus Room Figure I. The experimental setting was separated into the above seven rooms. 52 Slide Projector [:::::::::] Screen Response box Subject Figure 2. Typical experimental room, with the slide projector, screen, response box, and subject position labeled. 53 sat at one end of a table facing a screen placed approximately I8 Also on the table were instruction booklets, inches from the subject. a slide projector and response box. The earphones were hung on the wall next to the subject. Design Figure 3 is a visual representation of the design used in the study. There were four independent factors in the study: I) sex of subject; 2) contingency of strategy; 3) exploitativeness of strategy; and, A) or- der in which the two matrices were presented. The l28 subjects were di- vided evenly into the resulting I6 cells produced by the four indepen- dent factors of two levels each. In addition to the four independent factors, each subject was presented with both the 2x2 and 6x6 matrices. The resulting five factors of sex, contingency, exploitativeness, order of presentation and matrix size produced a 2x2x2x2x2 design with re- peated measures on the last factor and eight subjects per cell. Strategies The contingency of the other's choices and the type of Noncontingent. strategy, either exploitative or accommodative, produced four different For the two choice matrix the unconditional simulated other strategies. Alternative I was the cooperative strategies were easy to define. choice and the unconditional accommodative strategy was composed of that alternative on 85% of the trials. The exploitative strategy, however, was composed of alternative I on 15% of the trials. The six choice matrix was somewhat more complex since the defect choice was split into five different alternatives. For the six choice matrix the unconditional accommodative simulated other consisted of the COOperative alternative on 85% of the trials. The remaining l5% 5h .momocucocmq c_ muoomnzm mo Logan: sum: >v3um 0:» mo cm_mov ozu wo >m_am_o .m ocam_u Aw_v o>_umnoeeouu< _ acomcmucoucoz Ao_v o>~umu_o_QxM Ao_v o>_umnoeeoou< ; ANMV ucomc_uc0u Am_v o>_umu_o_axm Am_v o>_umvoeeooo< ANMV uewwe_ucoucoz Am_v m>_bmu_o_awm Aw_v o>_umv0EEouo< Amy umc_m oo_o£o m Amv umc_m ou_o;u N Amy umc_m oo_o;o w Amv umc_m oo_o:u N Amv umc_w oo_o:u 0 Amy umc_m oo_o;u N Amy umc_m oomoco m Amv umc_w ou_o;u N Amv umc_m oo_o;o w Amv umc_w oo_o;u N Amy umc_m ou_o;o o Amv umcmm oo_ocu N Amy umme QU_O£U m Amy umc_m ou_ocu N a: In: Um.— wL. GUwOLU umcmm ou_o£u fill _ Ao_v o>_uwu_o_QXm flame mm_mz _ ANMV ucomc_ucoo A:wv mmmeOm Aw~_v muummnsm 55 were spread equally over the five defect choices. Thus each alterna- tive was approved on 3% of the 100 trials. Thetnmonditional exploitative strategy was operationalized, not by splitting the 85% of the trials of defect choice over all five of the defect alternatives, but by choosing alternative "I," the "maximize The other 15% 0f the absolute gain" alternative, on 85% of the trials. trials had each of the other five alternatives equally represented. The conditional strategy for the two choice matrix was Contingent. In all previous studies more complex than the unconditional strategy. a contingent strategy was Operationalized by giving to the subject on trial n the response he made on some previous trial. Because a con- tingent accommodative and contingent eXploitative strategy were needed the tit for tat approach was not feasible. The contingent accommodative strategy for the two choice matrix was defined in the following manner: I) play alternative “I,” the cooperative alternative, until the subject defects for two consecutive trials; and, 2) after two consecutive de- fects choose alternative "2," the defect alternative, for two consecu- tive trials and then return to the cooperative response. This strategy was devised to give the impression of a COOperative other, but one who if the subject defected for two or more consecutive trials. would defect The contingent exploitative strategy for the two alternative matrix was, in a sense, a trapping strategy. The simulated other played alter- native "2," the defect choice, until the subject chose the defect alter- When the subject had defected for native for two consecutive trials. two consecutive trials, the simulated other cooperated for two consecu- and then defected again. tive trials, In surnma ry the contingent accommodative simulated other responded 56 to consistent cooperation with consistent COOperation and to defection The contingent exploitative simulated other responded with defection. to consistent COOperation with defection and to defection with coopera- tion. The contingent strategies for the six alternative matrix were simi- lar to those for the two alternative matrix. The exploitative and accommodative strategies were programmed to respond differently to the COOperative alternative. The contingent accommodative strategy re- sponded to the “cooperative" choice by the subject with the cooperative alternative while the exploitative strategy responded with the l'maximize absolute gain“ alternative. Both the exploitative and accommodative strategies responded to the cooperative choice by the subject on the trial immediately following the choice. The accommodative and exploitative strategies also responded differ- ently to the "maximize absolute gain" and "minimize risk" alternatives. The accommodative strategy responded to the “maximize absolute gain" If the and "minimize risk" choices with the absolute gain alternative. subject chose either of these alternatives for two consecutive trials the simulated other chose the "cooperative" alternative for two consecu- After the simulated other had responded with cooperation tive trials. for two consecutive trials it then returned to responding according to the choice made by the subject on the previous trial. The exploitative strategy responded to the "maximize absolute gain" in the same manner. If the subject chose and "minimize risk" choices either alternative, the simulated other responded with the "cooperative" alternative on the very next trial. If the subject chose either of these alternatives for two consecutive trials, the simulated other chose the S7 ”maximize absolute gain" alternative for two consecutive trials. After choosing the ”maximize absolute gain“ alternative for two trials the simulated other again responded to the choice made by the subject on the previous trial. The accommodative and exploitative strategies responded to the ”vindictive" and "maximize absolute gain" choices by the subject with the low risk alternative. Each time the subject chose the "vindictive" alternative or the ”maximize relative gain” alternative the simulated other chose the minimize risk alternative on the following trial. Both the exploitative and accommodative strategies responded to a ”behavior control” choice by the subject with the "cooperative" alternative on the following trial. In summary the exploitative and accommodative strategies responded on the next trial to the “vindictive,” “maximizing relative gain” and ”behavior control” choices in the same manner. It was in response to the ”cooperative," ”maximize absolute gain" and "minimize risk" choices that the two strategies differed. The accommodative strategy cooperated with a cooperative subject while the exploitative strategy exploited a COOperative subject. When the subject began choosing either the "maxi- mize absolute gain" or "minimize risk" alternatives the exploitative strategy tried to induce cooperation while the accommodative strategy punished defection. If the subject persisted in his choice, the exploitative strategy returned to choosing the "maximize absolute gain'I alternative and the accommodative strategy returned to making the "cooperat ive" choice. The exploitative and accon'modative strategies were designed to pre- sent two completely different images to the subject. The exploitative 58 strategy exploited cooperation but appeared to repent every time the subject chose the "maximize absolute gain" or "minimize risk" alterna- tives,