A m: .—.—‘--—— ——— CGMMUNECATIGN AND mam-MAKING: ‘ A STUDY OF THEIR :m‘ERmm m museum's; DILEMMA." ‘ AND OF CROSS CULTURAL DIFFERENCES ' Thesis for the Degree of M. A; MICHEQAN STATE UN‘IVERSWY DAVID J. F. BEATTY ' 1988 THESIS A... — ,4—0 In ,- 4‘ N “m. ‘ ‘I‘ _ _. ~- - v: ~ .- 4 ‘1'. q A I. ' .- ‘ .— - - ._. l a. “r Q ‘. J y“ ,, .- , I .Vbi :mwrm #3.. .' r.“ " '1'" ":Wl"‘fl’“‘vu ‘4'" . ’ ‘ :wune" . MSU LIBRARIES “a... RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped beIow. J HIV -: U 1;. fl 2’ COWIUNICATION AND DECISION-MAKING: A STUDY OF THEIR INTERACTION IN PRISONER'S DILH’MA AND OF CROSS CULTURAL DIFFERENCES By David J. F. Beatty A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Communication 1968 Accepted by the faculty of the Department of Communication, College of Communication Arts, Michigan State University, in partial fulfillment of the requirements for a Master of Arts degree. T c uh A 0411130.. CE. 5 ' + A A 0; ll". USPS w o , men it :-_ I 1M_!\yfi- a .5. -“r' V. Ld—vl \. lion i'zcl; . it 813%: C: ‘ZD‘H-..; 5L3 ~ ”13333 R- “’C‘ I;‘;'~. \LI"? ‘ ‘5' l‘ ‘L I‘E‘VQ“ . «sgcrqc ABSTRACT COM‘IUNICATION AND DECISION—MAKING: A STUDY OF THEIR INTERACTION IN PRISONER'S DILH’IMA AND OF CROSS CULTURAL DIFFERENCES by David J. F. Beatty If one considers Prisoner's Dilemma.Game (PDG) as a type of communication process where paired.players settle on certain patterns of interaction, interact in a series of decisions and communications, then it becomes important to isolate points in this process where important strategy considerations may be established. One communica— tion included in PBS by the experimenter is a.pause after 25 moves where the individuals are told their outcomes from.the last series of decisions. This pause provides time for an evaluation of past de- cisions and supplies specific feedback on one's own and the other's behavior. It is hypothesized that it will have an effect suCh that changes are more likely to occur at the first move following the come munications and the break than any other position in the 25 move runs. Past researCh by Martin (1965) with teams of three playing Prisoner's Dilemma.indicated that a deliberation does occur and that it significantly affects the strategy of the teams. The present study extends the explanation of the effect of deliberation to the individual situation. .A corollary hypothesis was also tested.which was intended to be an initial inquiry into the possibility of certain segments of the process being of significantly different importance for decision- meking. It was hypothesized that the section of moves 6—10 would represent a "hardening" level after the initial testing out of decisions David J. F. Beatty and would be significantly better at prediction than other segments of the sequence (tested against segments 1—5). An initial attempt to extend the testing of PBS to other nationalities was made with data being collected frCMIFrench and Canadian subjects. No hypotheses were made from.theoretical consider- ations of these cultures, nor were the samples representative of national populations. However, an explanation of the overall protocols was intended to pinpoint possible differences whiCh could be subjected to controlled study under more precise hypotheses. The subjects were 16 pairs of Canadian subjects and 1” pairs of PrenCh subjects. Research was conducted in a replication of Rapoport's 1965 study and some comparison drawn with that data. Results from.the first hypothesis reaChed significance at a level greater than p = .001, although a more precise focus on the effect of the pause on a continuing strategy, of different lengths reaChed sig- nificance varying from.p= (.10 to p= S + T. This ensures that it is more profitable to share rewards than to alternate between sucker's pay-off and temptation. Player One C1 D1 Rl Tl C2 82 SI Pl D2 —“—-.-0-1-0-0--.-0-0-0 T2 P2 Fig. 1B. Matrix of choices in definitional prisoner's dilemma. Also, for the sake of simplicity the matrix in the present study will have absolute values suCh that S = T. A.play of the game (Fig. 1B) consists of a Choice of a row (C1 or Dl) by Player 1 and of a column (C2 or D2) by Player 2, in— dependently and simultaneously, with no communication between them other than the fermal choices. The entries in the matrix are the pay- offs to the players, and are determined by the joint moves. In the same manner as Fig. 1A, the D move is superior an individual move no medter'What the other person does, yet the C move is better as a joint strategy. Prisoner's Dilemma upsets the strictly mini—max (minimize losses, maximize profits) strategy, and the "rational" strategy needs now to be defined with regard to context--that is, whether in the situation, it is more profitable to act from.a position of individual or mutual interest. It depends ...... The mathematical model cannot answer this u question. Since the behavior of the players determines which.may be most appropriate for the circumstance and the motive, there is no logical "right" answer. PDG is defined as a.mixed-motive situation since the goals of the players are partially coincident and partially in conflict. With this in.mind, move C has been termed a "cooperative" Choice, and D a "defection" or "competitive" move. Mutual cooperation is rewarded, unrequited cooperation is exploited, lone defection receives a bonus, and mutual defection is punished. However, these terms are extrapola— tions from.the theoretical model, and C moves may not be automatically equated across pairs, nor across time sequences. For example, McClintock and Messick* have proposed four dominant motives that might underlie choices in PDG. They are: (a) maximize joint gain: (b) efficiently pursue self interest. (C.moves), cm‘tfl nemdmfize own gain; and< FO>< .. \ 1\\ 7'4 JL Ir "" H) ' WW ‘y‘y‘y L——> ove Four r I . ,_ NMover V MoveN ‘_______Jl Fig. 2. Multiplicity of interaction of motive and move in PDG. predictability. Presumably it is the nature of the payoffs that tend to stabi— lize most interactions in a "lock—in" of CC or DD moves. One cannot afford to cooperate alone, and thus the resolution is usually a string of CC's or DD's. If the purpose of PDG is to find the most efficient way of promoting the learning of cooperation, then the dynamics of the bargaining interaction must be understood rigorously. The mathematical models suggested by Rapoport may provide this rigor, and as well, an understanding of certain structural aspects of the interactions may indicate key points of influence in the decision-making sequences. 10 The searCh for these key junctures is important since the potential range of interaction effects is so great. One needs tools to describe the interaction in meaningful ways. The first step towards this goal is a structural model. By taking the permutations of one move (CC, DC, CD, DD) as parameters, one defines units that seemlto reflect psyChological values. Underlying this model is the assumption that motivational pressures are reflected by monetary terms. Probabilities fer certain sequences and the breaking out of these sequences are computed. If the probabilities of the model con- ftmmlwell to the actual a.posteriori probabilities, then one translates these parameters into psyChological terms and can begin to construct a theory of cooperative-competitive situations. Once the dynamics of the basic model have been explicated, then one may begin to manipulate specific independent variables, such as communication possibilities, to see what outcomes are affected, and in what aspects the model should be adapted. Since the patterns are complex and extended, it may be that more than one model is applicable. It may be that human behavior in mixed—motive situations follows different rationales, and then it becomes the task of the experimenter to outline the conditions under whiCh one method of behavior is more likely to occur. The assumption of PDG is that game theory replicates elements of real life situations. This is not to suggest that the drastic simplification of the two—Choice PDG game duplicates real conditions, but rather that it provides some_evidence of what people do when faced with the Choice between cooperation and competition. The model has the advantage of getting vast numbers of replications easily under con- ll trolled and varied conditions, and the results, being stable, lend themselves to the formulation and testing of specific hypotheses. Answers from.PDG are not conclusions about real life conflicts, but sources of hypotheses about them. .As well, what is "simple" ftm*the experimentor to analyze is not so obvious to the subject. It is not immediately apparent what he is being "tested" forg and the costs and the consequences of eaCh session are established by the behavior of the subjects. The quickness of the decision may tap propensities that underlie more thought-out long term interaction behavior.* However, PDG is no panacea. The incentives and the diChotomous nature of the choices are not typical of real—life conflicts. Yet the perennial question of the validity of laboratory duplication of "real" life need not be discussed here. From.spontaneous comments of the participants, and observations of past experimentors, subjects g9_get involved, and it seems feasible that PDG taps behavior and.motivations that are fruitful fer the later construction of a theory of conflict resolution, and discovery of variables that facilitate the learning of cooperation. PDG in Recent Social Science Research The past analysis has outlined the traditional history of PDG research. There have been many variations in its use, but the emphasis has been on treating it as a tool to measure differences in certain populations, and thus have been concerned with the outcomes of the * . . As later theori21ng and results also suggest, it seems to be the case that the need to think out interaction strategies is also a variable that influences the fOrm of the outcome. l2 interaction. Studies by DeutsCh, Lutzker, Lave, McClintock, Harrison, Strand and Gallo have been of this general type. A.second emphasis has involved trying to understand the meaning of the game. This involves concentrating on the processes by whiCh certain states are reaChed. The interest of the game springs from.its foundation on paradox, that is, that a strategy to minize losses and maximize profits if adopted jointly will result in losses. The "opti- mum” strategy would result in a loss in a situation where there is an alternative available whiCh would lead to a profit. Therefbre, it is not clear whether similar outcomes represent similar processes. The attempt to find statistics that describe the game-playing behavior in categories that Chart the behavior and "represent" meaninngl psycho- logical properties has been most arduously pursued by Anatol Rapoport. His attempts to relate the behaviors over a long sequence to mathe- matical models represents an attempt to apply a probabilistic model to predict interactions in stress situations. The third emphasis, which has not been predominant in earlier literature, is an extension of the second, and quite different although compatible with the first. This approach views the PDG as simulation of a.communication situation.where two information-processing systems make decisions under the constraints of a mixed-motive contest and the past communications exChanged between them. It is interested in the process and rests on the assumption of the eventual success of Rapoport's approach: that the situation has a consistent logic whiCh occurs across different populations and is a valuable simulation of real-life "con— flict" situations. 13 I am interested in the communication patterns, and the interpre- tation of these patterns. The complexity of the interactions makes this task difficult. However, with messages limited to two choices (C or D), with all behavior available for accurate description by the experimenter, with the situation limited to one time span, PDG repre- sents an opportunity fer preliminary study of conflict resolution not affOrded by the much more complex level of interpersonal interaction. PDG presents an opportunity to begin to understand the gypamics of conflict, and the impact on systems involved in this type of situation. It differs from the traditional emphasis in that it is concerned with patterns as well as outcomes. The patterns are more basic, and if the path§_of the process can be traced to the point Where "key" decisions and interactions occur, then correlations with situational determinants and personality variables can be more closely tested. For example, it may be the inflexibility of the person low in trust, rather than his perceptions of the other player, that results in a low cooperative out— come. .A close analysis of the sequences would discriminate between these possibilities. Past studies, with few exceptions, have not attempted to isolate characteristics of the decision-making sequence to examine their impact on the rest of the process. Martin's study of groups (196M, unpublished) involved "group breaks," and obtained tape recordings of the decisions made at these pauses. This enabled the researcher to compare the type of evaluation that occurred with the subsequent strategies employed. The present study is an extension of that endeavor, and attempts to see to what extent the evaluation period as a structural aspect of the in interaction sequence affects strategies. This interest will be expanded in the following sections. Ckmmunication Processes Internal to PDG While past research has often concentrated upon using PDG as a tool to measure behavior in competitive situations, varying the con- ditions under Which it is played, often with theoretical hypotheses con- cerning the effect of these variables on trusting behavior (for which PDG protocols supply the statistics), there has not been equal attention paid to Prisoner's Dilemma as a communication situation. MuCh difficulty in analyzing the dynamics of communication is the variety of messages and the range of meanings potentially attached to them. This situation simplifies the problem by limiting communica- tion choices to two messages, and retains a resemblance to a.real life study by attaching rewards to the combinations of these messages. Both these facets of PDG are valuable fer using PDG as a researCh tool in communication researCh. The simplicity of the dichotomous choice does not mean that the outcomes are necessarily simple. If each.message is considered a step, or a building block in a series of messages, then the combinations of message elements can lead to complex patterns. The attempt to find patterns and changes in patterns is the task of the researCher. The more difficult task is then to assign "meaning" to these patterns, and begin to find which elements in this communication patterns are imp portant for determining subsequent messages. Thus, even with the Stark reduction of messages to two alternatives, the attempt to cate- ‘ gorize sequences and discriminate between patterns, is very difficult. 15 Each small addition to the breakdown of this complex process is usefu1, and provides a step for more specific testing of elements within the PDG at a subsequent stage. Involved in this notion is that each.message represents a de- cision on the part of the encoder. The message is considered a.reflec- tion of the decision. Thus, fer an analysis of the message sequences, inferences can be made as to the decisionemaking process going on "inside the head." Also since the consequences of the messages are assigned by the rules of the interaction, one is able to abstract from the question of content to the question of pattern. The reward or punishment compon— ent of the message are built in, and thus the results may be applicable to a vast array of communication situations that either have +/- come ponents, or one can look for the occurrence of similar patterns and infer to the +/— nature of their components. Since many uses of PDG have fecussed upon it as a.measurement of a relationship between two variables (e.g., trust and cooperative be- havior) they have emphasized the outcomes of the interaction. This approach stresses the dynamics of the process leading to that outcome, that is communication growth leading to end states of cooperation or competition. The PDG reflects a communication situation of interdependence. That is the outcome of the interaction is determined by ppth_decisions. This would suggest that the other's decisions are salient fer the de- cisionamaker and that probably he will be sensitive to the other's messages. Thus, rather than looking at messages as individual 16 creations, it is better to begin to consider relationships. The game presents a worthwhile opportunity to study the anfll-L cs of the rela— tionships as patterned by the communication behaviors , in _i_t_s_e_l_1: , apart from (or prior to) the situational variables that are brought to the situation. It seems to me that the game represents a good opportunity to study the dynamics of relationships and communications of itself, apart from the situational comrunication variables that have been manipulated in the past, and in a more basic framework where extraneous communications are eliminated. Each player brings a history and a "personality" to the situa— tion. This preSLmably is influential in the early choices of the game, but the clarity of this influence disappears with continued interaction and it is no longer as useful to correlate individual behavior (as if it were independent) with personality traits . Both players are given the same instructions and are limited to the same choice of messages over 300 trials (C or D). After each encoding, each receives feedback as to the payoff and the other player's message which was signaled si- multaneous ly . The interaction of these two messages produces the pay- off. Each is rewarded or punished depending upon the combination of the messages, and the "meaning" of these moves is dependent upon the structure of the rewards. Each move is a communication. Both are committed to a series of messages (interactions) such that over time each has the power to reward or punish the other. It is obvious that the messages may have both short term and long—term implications . To make this clearer by example: Player A may send out eight C messages which may establish a 17 credibility in Player B's mind concerning his trustworthiness. On the other hand, Player A might have Chosen D fOr a sequence of moves, earn— ing ten while his partner loses ten. This will result in a short-term profit but'may'Ctmmunicate to Player B that he is not worthy of trust. Thus, at a later stage, Player A signals (from his viewpoint) good in- tentions by Choosing C for some moves in a row. Depending on which of the previous sequences the game was played, Player'B will be more likely to take advantage of or to cooperate with this gesture. One can see how the initial Characteristics of the players are submerged. Studies with simulated cooperation (the other player is programmed befbrehand) have shown that these long-range patterns are significant in increasing the probability of certain moves (McClintock, Gallo, and Harrison, 1965). Contained in the data from.PDG then are all the messages that have constituted the interaction, and that have led to some form of resolution to the interaction. But the problem.is to decipher’and cate— gorize the "meaning" of this process. Some of the problems come in de- ciding within which framework a given move shall be interpreted. For example, the fifteenth move can be considered a communication: "I have chosen to cooperate (C)." It can be considered a feedback message, in response to Player B's last move: "Since you chose C, then I shall do the same." It can be considered a "feed-forward" message to the other player: "This is the way I shall play in the fhture as long as you also play C." Thus, what a move means to the participants is not clear. This is, of course, the same problem encountered in analyzing verbal communication, only there the message is so complex that one often stops trying to cover all the possibilities. In Prisoner's Dilemma, 18 the logical possibilities are overwhelming--2300! One needs to find certain "states" that are common to many pairs, and try to delineate the key points that lead to the arrival at these states. This approaCh has significant implications for the researcher. It breaks down the conventional distinction between dependent and independent variables. Each.move is both a.dependent and an independ— ent variable. That is, move 1H8 is to some extent (and the experimenter eventually wishes to determine how muCh) a.product of the last five, ten, or one hundred moves, and a determinant of move 149, 150, etc. with some undefined continued impact. The research scientist also changes from.the role of experimental controller to an observer. He has structured the situation within broad confines (e.g., matrix values possibilities for communication, nature of participants), but once the participants have begun to interact they set the patterns of that inter— action, and the sequence of independent/dependent variables. The implications for generalizability are interesting as well. The importance of the people and the situation are important in so far as they are conducive to certain messages initially being produced. This can be considered as related to the interpretation of the game. It may be that two "mediated" variables are important: Those that in- fluence the interpretation of the situation, and those that produce propensities for certain behaviors. Hewever, once initial behaviors (messages of cooperation or defection) have been exChanged, having reward/punishment consequences, initial intentions are replaced by re- actions to the specific situation. That is, however independently cooperative my nature may be, after a flurry of'D moves, I would 19 probably abandon the C response. Thus, a person may still be "co- operative," but the environment is so heavily loaded against COOpera- tive behavior that he adopts a new strategy which may be quite indepen- dent of his "normed? tendencies. The important point is that there are two types of generalizability: The effect of "external" Characteristics brought to the situation, and the generalizability of the model WhiCh records the sequences that result from.certain combinations of moves, regardless of player's initial traits. In the line of this second approach, different populations initially play the game not as much as to test for differences in traits of these populations as to evolve the structure of PDG. The internal interest in the model is to accumulate protocols across situations which reveal communalities and enable the researCher to concentrate on specific "situations" (e.g., the end of the interaction when "retribu- tion" is no longer possible) in order to single them out for more "real" and detailed testing. One is also interested in being able to predict from earlier patterns to the likelihood of later interactions. Testing the many possible (and probably meaningful) combinations is a lengthy task and it is important that the exact nature of the process being studied be determined. It may seemlsurprising to the reader that what has often been considered a simple tool for "measuring" trust has developed into a process model of communication in conflict situations. However, given its obvious limitations in describing real encounters in bargaining situations, it does provide the Chance to carefully examine the "raw" data of conflict.* *Footnote: A similar attempt at definition of patterns of communication 20 The stresses in PDG are similar to pressures in "real life" situations. Prisoner's Dilemma explores the basic motives involved in many of the current social problems involving breakdown of trust and escalation of ill feeling. The tenuousness of the agreement to co- operate and the difficulty in restoring mutual trust once the agreement has begun to break down are sufficient reason to study the variables involved in these situations. For example, it is reported that many White housewives are buying guns and being trained in their use. Once this message is conveyed to the negro, he begins to mistrust the motives of the other, and is liable to armlhimself. ‘What one does, the other cannot afford not to do. .As a result, the situation may quiCkly pass from a state of cooperation to competition with less than optimumlre- sults fer both. EaCh now stands the risk of being shot. What seemed a short term advantage (a gun for safety) in the long run has turned out to be a dangerous endpoint. There are other examples of the same sort. Two companies who share the market mutually avoid a price war even though as a short-term strategy reducing price would likely result in large gains fer one of the companies. Yielding to the short-term.temptation in this case is likely to lead to a lock-in at a muCh lower price, and both.will lose profits they now share. Union-management understandings also depend on a tacit c00peration Where a strategy fer short-term gain may degenerate by considering the individuals as infermation-processing actors is discussed in The Pragmatics of Human Communication. They suggest rela- tional regularities that cedar apart from.the content, and discuss sequences of behavior whiCh suggest a meta—communication understanding between the participants. Chapter II is especially relevant to the present discussion of Prisoner's Dilemma. 21 into a.mutual loss in the long run. The current newspaper strike in Detroit represents an instance where both parties are suffering heavy losses because they cannot find.ways to beat the competitive loCk—in. RiChardson's classic analysis of the armament race outlines the same pressures and balances. Both sides need to be on an equal footing, yet one is often tempted to try to gain an advantage in power over the other, and develops some extra capability that the other does not have. The other country must restore the balance, and thus a series of arms ament strategies ensue whiCh continually make the breakdown more severe and more dangerous. Many other examples could be mentioned to stress the precarious balance of cooperative positions, and the need for tacit agreement to cooperate. Since the social fabric rests on tacit understanding of What is legitimate, an exploration of the process by whiCh this understanding is generated, or the process by whiCh it breaks down, or the process by whiCh the cooperation is restored, is important. In this type of situation, the importance of the communication between the two participants and the meaning they attaCh to the other's behaviors seems evident. PDG is an attempt to study these variables in a simulated situation since the processes are often not manipulable in real—life situations. The Effect of the Twenty-Five Move Pause in PDG One of the assumptions in discussing PDG as a series of 300 trials has been that they are continuous. This is not accurate. Al- though most behaviors occur every 5-10 seconds, a procedural teChnique used by Rapoport results in an opportunity fer evaluation after every 22 twenty-five moves to check totals of the players. The impact of this period has not been discussed in the literature but would seem.to be important for the course of the decisions made. The pause and its communications may have two fUnctions. It provides time when the players can look at the outcomes of their last 25 moves, and take a break to decide how they may act in the next se- quence. .Also, there is new infermation put into the system. The in— dividual hears a total not only for his own performance, but for his partner's. The effect of comparison would seem to be more acute at this point than in the move-by—move evaluation of the participants. It seems plausible that the first moves after a "break" are likely instances for a Change in strategy to occur. Since the other'moves are more rapid, it is not as likely that a new strategy will be developed in the midst of the sequence. There is one earlier study that is particularly relevant to this examination of the pause as a variable influencing the type of decisions that are made. Martin (unpublished 196%) played PDG with groups of three per team. These teams had a short break after every 100 moves to discuss strategy. He found significant differences in.the increase of cooperative responses, and a decrease in the defection response. For example, at the end of 100 moves the proportion of cooperative re— sponses goes from .31 to .91. One of the advantages of the study was that it enabled Martin to examine some of the "internal" processes that occur in individuals in cooperative—competitive situations. From the group interaction a strategy is formed. It is interesting to note that the variable "group" made no difference from "stand " results 23 until after the break. It may be that two factors are operating in this situation: time to consider strategy, and others to discuss it with. In the individual situation this latter factor is ruled out, but not the former. The pause to total results increases the likeli- hood of a re-evaluation. In the individual situation, the only method of tapping this possibility, without interfering with the development of the interb action is to examine the behavior fellowing the break. If differences occur, it would suggest that the game is not a series of decisions with equal importance, but that rather, at certain points, the be- haviors have been re-evaluated and a "commitment" to a strategy made for the time period between breaks. These points would then become important for the injection of messages designed to influence the process. Martin also records some of the discussions that ensue at the break, and they are very instructive. They do mirror the psycholog- ical interpretation of game theoreticians, and suggest that Prisoner's Dilemma does mirror real life stresses and decisions.* *Sone of the communications between members are included in the study by Martin. They are interesting and are recorded here with permission of the author to clarify the PDG fOr those who are not intricately familiar'with its operation. Two categories of comments are listed below with examples: "Co-operation is the only way to win," and the conditional decision to cooperate. Two other categories were also feund, but with less frequency("teaChing commitment agreed upon" and "temptation to cheat."); "By 'Co-Operation is the only way to win' mentioned" is meant that at least one person in the course of the discussion said something to the effect that the only way his group could win would be to c00perate with the other side." 'Jeez! we've been screwing eaCh other. we should vote left all the time. It cost too muCh to be voting right all the time. we've already lost $1.38 in the first 100 plays.‘ 2’4 The impact of the pause will be less in the individual situation due to the absence of communication with other people but nevertheless may be significant. Also, since with the individual case the evidence for this process is not available the study must assume that the immediately fellowing behavior is indicative of the break. No delayed conditional strategy is observable in the present situation. This interpretation was tested by the fellowing hypothesis: Hypothesis One. Of all the times a change in strategy occurs in a bargaining situation, it occurs on the first decision following an 'If they play it smart they're probably saying the same thing that we 're saying: "Play it left until the other team.screws up and then go right." And if’we' re both thinking that way then we should both be playing left and we'll bOth make points. This way everyone wins. If'we start screwing them.they"re just . going to get mad and play right all the time and we '11 wind up . going down the drain at -9, -9. " Conditional Decision to Cooperate: it means that the groups agreed upon a strategy of cooperation, given that the other groups should turn out to be willing to cooperate. "Let's try left and if it doesn't work after three times then let's go right." "Okay. Let's play left for ten until they make a.move. We'll have to figure though that they're going to come baCk to the 5/l's again.hoping that we'll stiCk with the L's and they'll have a Chance of picking up 10. As soon as we get shafted though, let's switCh baCk to —9 until we've made up the ten points we've lost and then switCh back to a l, 1." "By teaChing commitment agreed upon" was meant an agreed upon decision to use some pattern of plays as a.way of communicating an intent to co— operate to the other group or as a way of teaching the other group that cooperation is the only strategy that makes sense. "Temptation to Cheat" means that at least some of the subjects in the . group explicitly suggested defection to be used as a.way of gaining extra points once it seemed likely that the other group was going to cooperate. 25 evaluation pause more than would be expected by chance. The probability of a change at move 1 is significally greater than at any other move in the sequence of 25 at the .05 level of significance. This break is an individual decision, and will be examined on an individual basis. However, the definition g strateg will be in terms of pairs . Thus, a change from CCCCCC to D will only be considered a change if the other player has not varied in his moves on the previous moves. If this restriction were not imposed, one would erroneously conclude that a D choice after six C moves was a decision to change, and if this came after a pause, one might attribute it to the pause. However, from Rapoport ' 3 studies , we know that interaction is more important than individual propensities , and in many cases the change would more accurately be described as a response to a move made by the partner the previous move . To avoid this error, patterns shall be defined as a sequence of four similar IE1; patterns of identical choices (CC, CD, DC, or DD). The stringency of the definition of strategy will be varied to 5 or more, 6 or more and 7 or more to see whether the definition thresh- hold makes any difference. However, each individual has the possibility of breaking the pattern and the move tlrat initiates the break from a strategy represents an individual decision. This is clearer after five similar moves since the constant input over five moves "suddenly" re- sults in a different response. It suggests that the individual has re- considered his response and has decided to try something else. The total N is calculated out of all the possible changes of strategy that do occur throughout the data, and the hypothesis is supported if the 26 proportion of changes on the first move is significantly higher than on any other move in the sequence. Since the decision to Change does not involve any commitment on the part of the decisionrmaker, there are two likelihoods of a Change in strategy. First that the outcome is favorable and that the pair continue in a favorable sequence or that the partner"s responses are not profitable for the decision-maker and he reverts to a safer or earlier behavior. His initial Change represents a "let's try and see" attitude and implies that the beginning moves of a sequence are the most flexible. Gradually the behavior hardens. By the tenth move he should have assessed the effect of his strategy and settled into an acceptable pattern. If this interpretation is accurate, it implies that by looking at the sixth to tenth moves one should be able to pre- dict the outcome of the remainder of the twenty-five moves significant— ly better than if one made the prediction at the end of five moves. Hypothesis Two: By observing the most frequent response in moves 6-10 of the 25 move sequence, one is able to predict behavior for the re— mainder of the sequence with a success significantly greater than prediction after five moves. There are two bases of prediction that can be used in this hy- pothesis. The first is derived fromlRapoport's analysis of the CD/DC combination as an unstable one since one player takes a continual loss at the hands of the other. If this is the case, then even.when these moves predominate in the 6—10 bracket it would.be a better prediction to look at the CC and DD moves as more reliable indicators. For ex- ample, with three CD moves and two DD moves the prediction would still 27 be that in the last fifteen the most common move would be the DD combination. The second prediction that can be used fellows from the argument that if a CD pattern has developed through to the end of the 10th move then it is sufficiently stable to continue through the 25th. Thus, eaCh prediction shall be made on the basis of these two criteria, and the two compared to see whiCh gives the better prediction. (1) The remaining fifteen moves can be predicted by observing whether CC or DD occurs more frequently than the other in the 6-10 sequence. (2) WhiCh- ever combination predominates in the 6—10 sequence, it shall predominate in the remaining fifteen. In case of a tie, the last move of either type shall determine the choice. The criterion for a successful prediction is that the predicted combination (CC, CD, DC, or DD) be the modal response for the remaining fifteen. However, once a permanent lock-in.has resulted (e.g., DD moves to the end of the game), results will not be tabulated since any segment of five would be equally usefu1 fbr‘prediction since there is no longer any variability in the outcomes. Discussion of TWo Internal Hypotheses If the first hypothesis is confirmed, it would suggest that a respite in a bargaining situation increases the likelihood of a.recon- sideration of strategy. In terms of the model of communication sug— _gested by PDG it suggests that the systems need time to program new strategies and make evaluations of their performance. It illustrates a recess in the interaction whiCh is easy to duplicate in other situ- ations, and may be useful knowledge for planning bargaining interactions. 28 In terms of understanding the model it draws attention to the fact that the sequence is not continuous and that a variable determin- ing outcomes may be the time available to consider strategy. If the model is being used over'many replications it is useful to understand as many sub-parts of it as possible. Rapoport in his statistical an— alyses has used sets of 15 moves to Chart the time course whiCh, while providing a finer time discrimination, perhaps Obscures meaningfhl de- cision units for the individuals. It is possible to examine this hy— pothesis within the context of a replication of his study without introducing manipulations that interfere with the other "external" variable questions, and there is no reason to assume that the other variable (nationality) would develop an interaction effect with this pause. Disconfirmation of the first hypothesis would indicate that major strategy considerations (if there are any) are made in the "heat" of the interaction, and that pauses, and the messages concerning the other's outcomes as compared to one's own, are not important in de— termining the outcomes of the game. Evidence from Martin's study indi- cates that a debate about strategy does occur in groups, and it is feasible that the same dialogue occurs within the individual. Since this internal discussion is not available as data, evidence that it has occurred.must be obtained by inference from.the first move following the break. A necessary assumption fer the measurement technique is that the decision.manifest itself actively on the first move, and not be of the conditional type. ("If'he does 'x,' then I'll do 'Y'.") The early trials are used to "test out" reactions of the other 29 player to the behaviors, and the maintenance of discontinuance of the strategy change is decided on the basis of these responses. However, in either case, a pattern develops by the tenth move, and there should be small likelihood of Change throughout the remainder of the sequence. If the utility of the 6-10 move segment is supported, it would provide tentative evidence for the position that decisions are made at the evaluation pause, and that the effects of this decision are recorded and acted upon early in the 25 series of trials. There is not much learning that occurs later, and one can safely predict outcomes at this earlier stage. External Variables: Nationality of Participants It is also useful to study the variables that are external to the inner process of PDG. Four classes of variables seem.to have re- ceived the greatest attention: "rule" variables, environmental vari- ables, strategies of the other player, and personality variables. In the first can be listed those variables that are concerned with the rules and payoffs of the PDG itself. Such Changes as increas- ing the discrepancy between rewards and punishments, making the payoffs asymmetrical (Solomon, 1960), have effects on.the outcomes. Often these variables have been manipulated along with other Changes and it is difficult to compare them. The current study will use Matrix 12 from Rapoport's 1963 study as reported in Prisoner's Dilemma. Matrix values will be 5, 5; +10, -10; -10, +10; and -1, -1. Environmental variables include such conditions as the possi— bility of communication (Loomis, 1959), (DeutsCh, 1958), the presence of a third party, (DeutsCh, 1960a), playing in teams, (Wilson, Chun, 30 and Kayatani, 1964), (Martin, 1964), and the nature of the instructions (DeutsCh, 1960a). The third type involves simulating the strategy of the other player at pre-programned levels . Potash and Wilson (1963) , McClintock et al (1963) attempted to find a difference between simulated coopera- tion and simulated defection but found little difference. An eighty— five per cent randomized "tit-fer—tat" programlwas found to elicit the most overall cooperation. The final kind of variable is the personality or nationality variable. The present study manipulates the nationality of the subjects. Results fromlplays with PrenCh participants are compared with Canadian results, and a preliminary comparison made with data collected by Rapoport and Chammah at the University of Michigan. Most tests of PDG have been done in the United States with college students. Since the game simulates a situation in which come petition and cooperative pressures exist, it would.seem feasible that the cultural attitude towards competition and COOperation might be a relevant variable in predicting the behavior of participants. The assumptions concerning what is "rational" behavior in suCh a situation may be confined to our way of looking at the world. The free enterprise views concerning open competition and enlightened selfeinterest may reflect themselves in playing of simulated cooperative-competitive , games. It may be very different in other cultures, particularly those with nonéwestern value systems. For example, in an Oriental culture, the emphasis placed on interaction in such a situation may be upon the relation between the participants rather than the outcomes (profits) 31 of the play. Avoiding making the other lose face may be the purpose of the social encounter rather than protecting one's investment in an economic encounter. It is possible that the differences might exist in two areas. The first is the interpretation of what constitutes a situation of co- operation and competition; and the second, is the interpretation of what is proper behavior given that the situation is of a competitive- cooperative type. In the first mode, one would expect participants to begin in a consistently different way; in the second, one would expect different patterns of behavior to develop. Since the testing of Prisoner's Dilemma Game has been done in this culture, where the analy- sis of the game in the literature oddly resembles the prevailing phi- losophy of "economic man," it would seemlparticularly apt to extend the range of the model's testing to areas in which this philosophy is not so accurately reflected in the cultural norms. This is especially true since the game has been.used to simulate international situations. The first method of testing is to fellow Rap0port's advice and Choose homogeneous pOpulations (e.g., Japanese playing Japanese) before continuing to study the outcomes when different nationalities play eaCh other. If'perfOrmance by different populations is the same, then one might assume that results from.PDG found in United States are not likely to differ significantly from what would have been found else- where. One would know that the stresses hypothesized to be Operative in PDG are not merely a reflection of our particular cultural assump- tions concerning motives in competitive-cooperative situations. If there did appear differences, then further studies could be develOped 32 to closely test the specific divergencies. Since the number of studies with PDG has burgeoned to the extent that the Journal pf_Conflict Reso- lppipp has had to declare a moratorium.on publication of PDG results, it seems that the test of its ethnocentricity should be perfbrmed. It is important to note that the study does not begin from.a theoretical hypothesis about culture, although fromla.comparative socio— logical point of view this would be preferable. To look fer differences and find them as result of a theory of the particular culture is much more productive than conducting studies between "different" "cultures," and then attributing differences to the "cultural" trait. In the present study, no inferences will be drawn from.the results to cultural characteristics, but will be tendered as exploratory groundwork for (1) extended testing of specific segments of PDG. One could then, with more precision, construct an experiment to examine particular'differences; (2) if no differences are found, to suggest that results from PDG are not necessarily restricted to United States; (3) if differences are found, to discriminate whether the difference suggests "cultural" dif- ferences in.attitudes towards cooperation and competition, or whether PDG, as a.measuring instrument of cooperation and competition, is not applicable in some other countries. A.study of the impact of nationality (cultural) differences on PDG, and by inference on behavior in competitive-cooperative situations, would require representative samples. The assumption in the present study, given the non-representativeness of the samples, is that cultural attitudes underlying all sub-sections of the culture are significantly different across cultures and offsets the range of individual differ— 33 ences within that culture. This assumption depends on the belief that culture is a.more powerful predictor of attitudes than any of the un- controlled sample-specific traits within the culture by whiCh the in- dividuals might be distinguished. It would have been preferable to matCh individuals for personality characteristics theoretically relevant to cooperative behavior, to have Chosen representative subjects from the country, and then have had themlplay PDG. This was not possible. If the samples do not Show differences, one is more certain of the reliability of PDG. However, if there are differences, it may be due to the presence of "hidden" variables that is present in different proportions in the sample. If these hidden variables are peculiar to one culture, then the results reflect a valid difference and further tests should confirm the fact. The results of the study would be use— ful evidence in searChing out these possibly relevant cultural differb ences. There is also the possibility that interaction effects between culture and uncontrolled variables may mask legitimate nationality dif- ferences. This is a risk, but the low number of personality variables that have been significant variables in PDG lessen the chances. With these rudimentary goals in mind, a program to test the be- havior of Japanese, FrenCh, Indian and Canadian participants was set up at a young adult camp near Expo 67. At the time of the proposal, conferences of all four nationalities were scheduled for the camp. However, neither Japanese nor Indian conferences completed their reser— vations. This left the two "western" samples and curtailed much meaningful cross-cultural comparisons. The study reports the results from the portion of the nationality samples that were available. The 31+ outcomes are exploratory, and tentative comparisons with previous U.S. data will be made. No hypotheses as to the nature of the differences that might be found between the two populations have been made. Maj or attention is devoted to the analysis of the internal communication process, but a report is made of the between sample differences in cooperative outcomes . CHAPTER II METHODOLOGY The study was conducted at a YMCA Young Adult Camp near Montreal. Subjects for the PDG were volunteers who filled out a request ftmmlat the office upon registering. Subjects Members of the Canadian sample were obtained during a one and a half month time period. Two methods of obtaining volunteers were used. The first was a small notice that was handed to eaCh guest as he/she filled out registration, indicating that the camp was sponsoring a study in "problemrsolving" whiCh would pay the volunteers a $1.35 base scale wage with the chance of earning more. Also, since most of the _ guests came on weekends, either the experimenter or the Camp Director made a short announcement Saturday morning repeating the infOrmation from.the registration circular and asking that persons interested in helping out contact the author afterwards. The FrenCh sample were recruited in a different manner. They were a group of 50 young people traveling together~through Canada in connection with Centennial Year and were in the Camp fer three days only. The leader of the group was contacted and helped obtain subjects. This was facilitated by the group rates they had received and was done as a personal favor to the Camp Director. In neither case was any mention made of the nature of the study. No mention was made of cooperation or competition. In the Canadian sample, some subjects may have known that the experimenter was working 35 36 on a degree in the field of "Communications," and hence might have tried to second-guess the game from.that point of View but this was un— avoidable and was thought preferable to duplicity. Sice the study was held in a camp setting there was no way of . guaranteeing that contamination would not occur. However, due to the slump in attendance it seldom happened that more than two or three pairs of the Canadian subjects were run in the same weekend. It seems unlikely that there would be a carryover effect outside of the weekend since the subjects came from.different areas and the likelihood of interaction outside the camp small. When the game was finished and questions were answered if the participants Wished, they were asked to refrain from discussing it with others. No evidence appeared that this request was not followed although other.members of the staff were asked to report it to the experimenter if they did observe this happening. No subjects reported having played the game befOre. The FrenCh sample was in one group and were run in three days. Again reliance on the promise of the participants was the sole guarantee of independence, and it was more difficult to CheCk since many of the staff did not have a facility in FrenCh. All Canadian pairs were assigned under the circumstances that each did not know the other. As far as possible subjects were not told Whom they were paired with beforehand, and questionnaire replies indi— cated that in no instance were friends matChed. Four of the sixteen pairs were female. Since the French sample had been traveling together for a.month, strangers could not be paired, and the effect of this variable is 37 indeterminate. Seven of the fourteen pairs were female. Both samples were of young people, with the Canadian sample being older and having a heavier weight of males than the French sample. The average age fer Canadian 38 was 2H.2 years old. The aver- age age for FrenCh participants was 19.1 years old. The Canadian sub- jects had a mean of 13.9 years in sChool, and the FrenCh 12.8. .A final complication needs to be treated: the French participants knew eaCh other prior to the PDG. Neither sample can be considered to be a.random.sample repre- senting a specific population. However since the major internal hy- potheses are concerned.with the behavior of systems in a conflict situation and contain both independent and dependent variables withip' this sequence of messages generated within PDG, the non-randomness of the sample does not affect the testing of Hypotheses One and TWo. In regard to the comparison of the populations with eaCh other and the Rapoport findings of American College students, the study is meant to be exploratory in pointing out areas of finer examination that need study. The Experiment Incentives The subjects were paid $1.35 per hour eaCh for participating in the experiment. This was paid in the form of a deduction from their room.and board. It was possible for the subject to win or lose an amount of money roughly comparable to what he was paid for the session. For ethical reasons, it was not desirable to have the subject leave after having suffered a loss greater than his pay, that is, in debt to 38 the experimenter. This eventuality never occurred, and the methods outlined by Rapoport (1966) to correct this did not need to be used. Setting The plays took place in a lodge separated from the rest of the camp. The subjects were asked to report to the lounge of the lodge and then were brought to the room and asked to Choose one of two seats. Thus the subjects saw eaCh other prior to the start of the experiment and probably exchanged a few words. Since, however, the nature of the experiment was not known to them until they were seated in the experi- mental situation, they could not discuss the experiment before the session. The pair of subjects were seated in adjoining desks but separated by a partition that prevented any communication between them. They could not see each other, but both could see the experimenter and could be seen by him. See Fig. 3 for details. Instructions After the subjects were seated (Choosing the seats as they wished), they were read the following instructions by the experimenter. "You will be playing a game which.has certain payoffs. You can- not by yourself control the specific payoff for a given game. Rather, the outcome will depend on what your partner does, as well as on what you do. Each of you.has a payoff sheet in front of you. The game is played as follows. You are players A.and B re- spectively. In front of you are two cards, labeled 1 and 2. On any given trial eaCh of you.may play by pointing to either the card numbered 'one' or that numbered 'two.' Any decision is final. You cannot Change 39 P Player A L Player B Y W , O E rm 0 /’ D P A (Cards to which R 8'3 pointed to T indicate choice I of move where T C = 1 I D = 2) O N EE .E //‘ Experimenter (Cards used by experi- menter to relay choices of S's after both had chosen.) Fig. 3. Organization of room for Prisoner's Dilemma Game. your mind once you have pointed to a card. The payoffs resulting from such a move are indicated in your payoff sheets. For example, if you both choose 2, each loses 1 point. If A chooses l and B chooses 2, A loses 10 points and B wins 10 points. If A chooses 2 and B chooses l, A wins 10 points and B loses 10 points. If you both choose 1, each wins 5 points. Each point is worth 1/10 of a penny. During the course of the to experiment you will play this type of game a large number of times, i.e. , for approximately 1 hour. Each player's total gains and losses will be added together at the end of the experiment and converted into money . The experimenter will signal after each move the number of points gained and lost by each person. Each of you will then record your particular gain or loss on the record sheet in front of you. After each series of 25 moves you will be asked to total your gains and losses. It is of the essence ttat you do not communicate with each other in any form whatsoever. This includes sighing, laughing, or any other form of communication which might indicate how you feel about given out- comes , or how you would like your partner to behave . The reason for this condition of _n_o_ communication is that the experiment becomes use— less for my purposes should any communication take place. In view of this , it will be a condition of the experiment that the experimental session be disbanded without compensation to the subjects for time put in should communication between grotp members occur. The same condition holds if a subject leaves the experiment before it is completed. The gains or losses accumulated by each of you by the end of the experiment will be added to or subtracted from your hourly pay of $1.35 per hour. Please DO NOT TALK about this experiment to others . They might participate in later experiments , and they might be influenced to play differently if they know about it." Following the instructions the experimenter answered subj ects' questions , if any, and examples of the choice options were reiterated to clarify what was expected of them. In answering the questions care H1 was taken to avoid giving the subjects any impression as to whether they are "expected" to compete or to cooperate. The only points clari- fied were those having to dO'With what happens, depending on each of the f0ur pairs of Choices whiCh are possible outcomes of a play. Any other probing questions by the subjects were parried with non-commital replies, such as "Do what you think is best" or "It is not possible for me to answer that question at this time." These instructions were taken from.Rapoport's report of his Methods and Procedures and are similar~with small differences.* The “‘ setting of the room in a conference setting was most likely different from.the fbrmal laboratory at University of MiChigan. .Also Choices were labeled 1 and 2 instead of left and right as in the former study. Procedures EaCh subject now had in front of him a game matrix (Fig. 5) two cards labeled 1 and 2, which he used to indicate his Choices to the experimenter, and a score sheet, (Fig. 6). In the experiment, the two cards, representing the subjects' Choices were labeled 1 and 2 and placed on the subjects left and right in no particular pattern. Rapoport's study had labeled his cards "left" and "right" and they were always placed in the same place. Rapoport felt this may have led to a bias; however, it did not seem to be significant import to have perpetuated the error merely fer the sake of replication. * . For the French sample the instructions were read 1n FrenCh, and the experiment conducted in FrenCh, with a French interpreter from the Camp who had previously been taught the game. 42 The subjects made their Choices at a signal given by the experi- Inenter. The signal word was "next." The subjects made their Choices known by pointing to one or the other card. Thereupon the experimenter signals what the other has chosen and announces to the subjects what each has won or lost on that play. For example, if Subject A chose "1" and Subject B Chose "2" when both Choices had been.made the experimenter would relay the Choices by pointing to the cards on his table which were visible to the partici- pants, and would say: "Minus 10 to A, plus 10 to B." .After the experimenter announces the result, eaCh subject enters his own gain or loss on his score sheet, (Fig. 6). The experimenter likewise records the outcomes on his own data sheet. The outcome CC is coded as "1," DC (2 by.A, l by B) as "2," CD (1 by A, 2 by B) as "3," and DD by "4." .After the subjects and the experimenter1have made their entries on the score sheets, the experimenter gives the signal fer the next play. The timing is easy. That is, the subjects are not rushed to make their choices. As the game progresses, it takes only a few seconds on the average for eaCh Choice, since there are no calculations tt>make but only possible "policies" to follow. If the subjects ask whether they may use their score sheets to keep any other records or to make calculations (whatever they are), they are told that they may. However, this seldom occurred. After each 25 plays, each subject adds up his gains and losses cumulated over those 25 plays, and after eaCh 100 plays, the gains and 43 losses are cumulated fOr the 100 plays. The experimenter also adds up the gains or losses and compares his results with those of the subjects. To save time and arguments, discrepancies of no more than 3 points are decided in favor of the subject. (Note that the gains of one subject need not correspond with the losses of the other.) Larger discrepancies were checked by recalculation and corrected. This occurred more fre- quently than was expected. Following the experiment, each subject filled out a short ques- from; . tionnaire, in which he answered questions about what he was trying to 1 accomplish; what strategy, if any, he employed, and what strategy he i thought the other player employed. The experimenter's score sheet, specifically the sequence of code numbers, representing the sequence of outcomes, constitutes the raw data of the experiment. Three hundred plays constituted an experimental session. Statistical analysis of the collection of protocols yields the processed data. The details of this approach are outlined below and are developed from the teChniques reported by Rapoport and Chammah in Prisoner's Dilemma. NUmber of Replications In this approaCh the researCher concentrated on the regularities which can be brought out as a consequence of the law of large numbers. iLittle attention was paid to the performance of any individual. Rapoport considered ten pairs a minimal number for’reasonable statis- 'tical stability. The FrenCh population consisted of 14 pairs, and the Canadian sample 16 pairs. Both were combined as one sample to test the internal hypotheses concerning the effect of the pause, but the sample nu size of significant "changes" was calculated out of that number that net the criteria. The sample size (of the "pause" hypothesis) was determined by tracing through the protocols of the thirty pairs of subjects to find all instances that net the criteria of significant changes of strategy. With the criterion level set at fOur identical patterns, the total N occurring was 292. With the criterion level tightened to five ident- ical patterns, the N was reduced to 190. The N for the testing of the hypothesis concerning the predic- tive power of the 6—10 sequence of the twenty-five move format Should have been 30 pairs x 12 (sections of 25 per 300 trials). However, the restrictions concerning "lock-ins" (where the remaining responses fOr the rest of the game are of one kind), reduced this N to 255. The N fOr comparing French and Canadian samples was of course, the fourteen and sixteen pairs of eaCh that were available for testing. It was difficult to test fOr significance with this N but there was no alternative. Statistics Hypothesis One: Changes in strategy occur on the first move fOllowing an evaluation pause significantly more times than on any other move in the 25 trial sequence. f(SMl)i> f(SM2):> ...f(SM25); where f represents the frequency, and SMn represents the strategy changes at Mbve n. Null Hypothesis: there is no difference in the expected number of strategy Changes for eaCh of the move categories, and any observed us differences are merely chance variations to be expected in a random sample from.the rectangular population where: f (8M1) = F (8M2) = ...f (SM25). Level of significance will be alpha = .05, and the N for the sample will vary with the number of strategy Changes that occur within dif- ferent ninimum.definitions of what constitutes a strategy. Where stra— tegy nininunlis u, total observed N # 290; where strategy minimum is 5, N = 190, where it is 6, N - 1H2, and where the minimum.strategy length is 7, then N = 109. The sampling distribution of X2, as computed by, x2 = z_<01 -Ei -.5)2 Bi follows the chi-square distribution with df = l. The Yates correction term is included since only one degree of freedom is present. The lower limits of what constitutes a "strategy" have been arbi- trarily varied from.four to seven to avoid overlooking possible signif- icance from a narrow conception of what represents a strategy. .A strategy is defined as a pair measurement, although psyChologically a strategy is a.decision by an individual player. Both participants must engage in the same response befOre a Change in move is said to indicate a Change in strategy. Since the data are not continuous (e.g., 2.5 strategy changes are not possible), a X2 statistic was preferred to the Z test for pro— portions. For purposes of testing, the categories were reduced to two: the category Move One, and the category not-Move One. Average observa- tions were computed for the remaining 24 categories, and entered in this latter category. Fig. H indicates that this non-differentiation us of the 24 moves did not violate any meaninngl differences among the remaining1moves. Three requirements for the X2 test were met by the data: a large N (109-290), eaCh and every sample observation occurring in one and only category or class interval, and eaCh observation being statis- tically independent of the others. This statistical independence ob— tains in the instance of strategies since knowing that one strategy is occurring tells nothing about the occurrence of any subsequent strategy. (p (strategy 2) = p (strategy 2)/strategy one).) This is very differb ent ficmlnaintaining that the moye§_are independent, since the founda- tion of PDG and its interpretation is the impact of previous messages and decisions on the probability of the next move. Hypothesis Two: The most frequent response type (CC, DD, or CD/DC) in moves 6—10 predicts behavior correctly for the remainder of the 25 move sequence significantly more often than does prediction after moves l-5. f (pr. 6—lO).> f (pr. l-5) .Null Hypothesis: (Ho) There is no difference in number of successful predictions in predicting from.moves 6—10 than in predicting from.moves l—5. f (pr. 6—10) = f (pr. l—5) Let the significance level be alpha = .05, and N = 103. All instances of both predictions being correct or both predictions being incorrect are not included in the Chi—square statistic and are considered null cases. See Table 3 for the breakdown of these categories. The sampling distribution of X2, as computed from the forrrula in w'tm v . . .1 . H7 in Table One, follows the Chi—square distribution with df = 1. As discussed Chapter I, this hypothesis is based upon the inter— pretation of the sequence of decisions where the pause represents an important decision—making point fOr the players. If he has opted for a change in strategy it should occur in the first few moves. When it has occurred, presunably the player assimilates the feedback to this change and acts accordingly in continuing the strategy or reverting to another fOrmula. By the tenth move he should have made his judgment as to the reaction to his decision and have adopted a style in response to that communication. However, it is possible that this could happen sooner than the tenth trial, and the recording of the first five trials may reveal this contingency. It may also happen later, but if this were the case, it would not be useful for prediction purposes since little economy would be gained the closer the "hardening" point is to the end of the sequence. A.further separation in the analysis is made in terms of the criteria for what will be considered the most frequent response. RapOport argues that the CD or DC combinations are unstable and tend to disappear quickly. If this is accurate, then a predominance of CD or DC moves at an early stage (6—10) is likely to disappear and the later parts "harden" into a DD or CC majority. By this reasoning, one 'would note which of the CC or DD moves are the most frequent and base the prediction on this regardless of whether there are more CD or DC combinations. On the other hand, by the "hardening" notion, it would seem that if a CD/DC response is sufficiently frequent at the 6-10 level to 1+8 Table l. Chi-square results of obtained frequency of changes in strategy at move one vs. all other moves . (l) (2) (3) (H) k Formula: X2 = 2— (Oi - Bi)2 df i=1 Ei ll l—' With 3 as cut-off level. x2 = (u8 —ll.6 — .5)2 + (242 -278.u -.5)2= 115.7 11.6 278.u With _5_ as cut—off level. X2 = (37 —7.6 —.5)2 + (152 —182.u —.5) = 122.3 716 182.u P = < .001 With _E_5_ as cut-off level. x2 = (32 —5.7 —.5)2 + (110 4136.3 — 5)2 = 121.7 5.7 136.3 With 1 as cut-off level. x2 = (30 -u.u —.5)2 + (79 -104.6 -.5)2 = 1n9.2 u.u 10u.6 P = (.001 be in the majority, and this level is the decision level, then they should remain the most frequent . Both these possibilities will be examined to see whether there I+9 is any difference in predictive power between them. Since there are many combinations that can occur, the alternatives will be reduced as follows . Rapoport Prediction: Rules Whichever of the two categories, CC or DD, has the most occur- rences will be the most frequent of all categories in the final fifteen. When the two categories, CC and DD, are tied, that which occurs last will be most frequent in the last fifteen. When neither of the two combinations occur in 6-10 (l—S) , no prediction will be made. If in the last fifteen moves, the predicted combination is tied with another combination it will be considered in- correct. The categories CD, DC, will be considered as separate categories for adding frequencies , but are interchangeable for prediction. For ex- ample, if in the last fifteen moves, there had been CC = 6, CD = ’4, DC = 3, and DD = 2 , CC would be considered to dominate even though com- bined the "unstable" categories, CD/ DC would have a higher total. Likewise, if the prediction is made from a predominant DC combination in the predictive sequence (6-10 or l--5) it will be considered correct if either DC or CD has the most responses in the last-fifteen. When the pairs have locked in upon a response for more than 25 trials, the analysis will not be entered because it makes no sense to describe the predictive power of a part as if it were a function of position. Any position in the sequence would be equally good for pre- diction. It would, of course, increase its statistical significance to include these occasions , but practically it would be of no use. 50 {ples for Unstable Prediction Whichever category CC, CD/ DC, or DD has the most frequent hoices in trials 6-10 (1-5) will also be the most frequent in the last fifteen trials . When two categories are tied in 5-10, the one with the last position will be used to make the prediction. The CD/ DC category to successfully predict must have one of its two cells the most frequent and not its sum total of the two. It is correct to make the prediction on the basis of the CD mode in 6-10 and have the DC combination the mode in the last 15, and still consider the prediction confirmed . If there is a difference between these two bases of prediction, it would indicate either that the instability of the CD/ DC move is a significant characteristic of systems behaving in competitive-coopera- tive situations , or that it is not . The former case would cast doubt on the notion that subjects lock in because they cannot take continual punishment, and would suggest that during the "learning" stage of the interaction, all types of moves are incorporated with the same flexi- bility and likelihood of continuing . The above rules also apply to the consideration of the predic- tive power of the 1-5 sequence. Method of Comparison over 300 Trials Rapoport and Chammah in Prisoner's Dilemma (1965) outlined dif— ferent series of statistics which might differentiate populations play— ing PDG. This was done in terms of both outcomes and in terms of probabilities of certain sequences occurring. The latter was the more 1 .,‘_‘1 Ii’j'im 51 discriminate analysis and was used to describe processes that led to different totals between male-male, male-female, and female—female pairs. It was at this level that mathematical models of the stochastic type, or Markov Chain.probabilities were introduced. They are not used in analyzing the present data since the size of the sample would not provide the stability for this depth of analysis. Another criterion for the statistics that were used was their potential utility as intriguing psychological variables. Below is a discussion of the statistics Rapoport uses, and those fOllowed by an asterisk are used in the current experiment. The cooperative move is labeled C, and the competitive move (or defection move) labeled D. With the pair as the unit of analysis, there are sequences of pairs of CC, CD, DC, or DD. Comparison between populations can be made with the following indices. (a) * the average frequencies of the four pairs over the 300 trials. (b) * the average frequency of the C Choices. (CC + (CD ¢ DC/2)). (c) * the time courses of these frequencies (a and b) broken into 15 trial blocks. (d) * variances of these frequencies in a given population. If these indices are identified with motivations as Rapoport tends to do, (e.g., a high C percentage indicates "trust."), then it is possible to compare populations on these gross indices and suggest areas for detailed study that resemble psyChological motivations and attitudes. MOre particular segments of the process can be measured in order 2 52 to concentrate upon the meChanics of learning cooperation. (e) (f) (s) * statistics Cl and C2 represent the prOportions Choosing cooperatively on the first and second moves of the game. By measuring the fraction of the population whiCh decided upon the cooperative Choice on the first or second move, some evidence as to whether populations approaCh the game differently or whether after interaction differences appear, can be obtained. * P(o) measures the correlation between players' decisions. To the extent that one player's Choice matChes the other's, they will be correlated. If P(o) is near zero, there would be no evidence that the decisions of one player affect the other's decisions. The nearer P(o) is to -1.00, the more evidence there is for the statement that cooperation on the part of one member of a pair tends to elicit cooperation on the part of the other, and similarly for defection. If P(o) is negative this would be evidence that cooperation on the part of one member of a.pair tends to elicit defection on the part of the other and vice versa. On a priori grounds, positive, zero, or negative values of P(o) seem plausible. P(l) represents the case where the moves are correlated with the prior move of the other player. This can be done any length back into the series, but becomes complicated. Most frequently, P(l), a coefficient with a built—in shift, is used. 53 The following discussion indicates how precisely it is possible to explore the decision—making and communication process with a mathe— matical model. The results of the current study will not be processed through this model stage unless initial results reveal worthwhile sig— nificant differences between samples. (h) p(Cl/C2) or is used where C'2 refers to the other's choice on the immediately preceding play. This measures the probability that a given subject responds cooperatively fOllowing a cooperative response on the part of the other. (i) = p (Cl/D's) and is a measure of the tendency to co— operate in spite of the other's failure to cooperate. The two quantities just defined relate to responses to the other's choice. Corresponding indices relating to one's own immediately preceding Choice can be defined. (j) = p (Cl/C'l) measures the persistence of the cooperative response. (k) = p (Cl/D'l) measures the nonpersistence of the defec- ting response. Rapoport labels the above indices "response-induced" indices. They consider the impact of the other on the individual. However, his interpretations of the game suggest that statistics relating to the pair are more meaningful and he develops what he calls "state-condi- tioned" indices. (See Chapter 5, Prisoner's Dilemma, 1965) (l) x = p of a C following a CC response. (n0 py = p of a C following a CD response. (n) z = p of a C following a DC response. (0) w = p of a C following a DD response. 1 i!" ‘Wh. _.. 511 These conditional propensities are also psychologically sugges- tive. For example, "x" refers to the probability of Choosing cooper— atively after one has cooperated and been rewarded. This suggests a resistance to the temptation to defect; hence, is called an indicant of "trustworthiness." "y" refers to the probability of Choosing c00per¥ atively after one has cooperated and been punished. This may suggest either~"nartyrdom" or persistent belief in teaChing by example, or per— haps "forgiveness." "2" refers to the probability of Choosing cooper- atively after one has defected and got away with it. This propensity may suggest "repentance." Finally, "w" represents the probability of shifting to the cooperative choice after both.have been punished for defection. Since there is no point in shifting to the cooperative Choice from.DD unless one hopes that the other*wi11 do likewise, the propensity "w" suggests "trust." These latter statistics can be computed from the observation obtained, but are not likely to be different unless the outcomes are different. If the need arises, they can be included in the analysis. CHAPTER III FINDINGS Hypothesis One: Changes in strategy occur on the first move f0110wing an evaluation pause significantly more times than on any other :move in the 25 trial sequence. f(SM1)> f(Sm2) > ...f(SM25). To review briefly: a strategy was defined as a consistent :manner of interaction over a number of moves by both.members of a pair. If only one player's behaviors had been considered, then a."change" from a sequence might have been the result of the other's previous move, and not an independent internal decision. For example, in Fig. u, two ;possible interaction are recorded. In the first there is no new come mmnication from.the other player and thus it may be considered an internal evaluative Change that led to the move "D" by Player B. In the second, neither of the two "D's" by Player A.or by Player B can be Player A Player B (b) Player A Player B C C C C C C C C C C C C C C D C C D C D Player B has made a change Player'B has not made in strategy a Change in strategy Pig. 4. Definitions of strategy for Hypothesis One. considered legitimate changes by the definition. The "D" by Player A had a history of only 3 paired moves before it, and thus a strategy could not be considered fOrmulated, and the "D" by Player B was made 55 56 in response to the previous change by Player A. The threshold criterion for when a sequence would be considered to reflect a strategy was varied from.four to seven, with statistical comparisons being made at eaCh level. In each case, the definitions was formed to read "four or: m paired consecutive similar moves," such that the strategy might stretch to any length until it Changed or the game finished. With this definition, it was possible for a stra- tegy to start anywhere and finish anywhere. The hypothesis is not con- . ."fe :J‘E - '3‘ _ cerned with where a strategy first coalesced and became behaviorally recognizable, but with the idea that the communication pause would pro- vide an intervention into the decision-making process which would be likely to change any present strategy, if_there were any tendencies to change. Since the interest of the hypothesis was to compare the first move with any other, X2 was computed by taking the remaining 2H cate- gories (2—25) as one category and comparing obtained with expected values. Fig. 5 indicates that this collapsing of categories did not conceal any differences between the 25 moves. Table 1 shows that fOr all definitions of strategy the results were highly significant (with a.probability of less than .001). The evaluative pause and communications during that pause presumably af— fected the immediately following decision. However, lacking a control group with no pauses nor feedback, it is not strictly possible to assert that without any pause the 26th ...515t...76th...276th.moves would not in any case have been prediction points for Change. It does seem.very unlikely. mm :m mm mm Hm (Cw 57 (ma i ii. .‘hw. UM. . .ih_ may 5H I} . l oH mH :H .o>oE\mcmomco >mmeospm mo .2 .m .wam mat NH HH‘ DH m omvoomxo I u I m. h o m :. m N H ' ‘I ‘l' I - '1 .‘r ‘ l‘ I ll, ‘ ‘ COLOZI‘NO «H :H oH ma om NN :m mm mm om mm :m mm mm o: N: a: o: _m: om U)+'$-er0-P3 UFCFUCbOmm O'H :z 3 E.Q o 9 58 Confirnation of the main hypothesis indicates that knowledge of where a pause occurs is useful information for predicting where stra— tegies are most likely to change if they are going to_ghange, It does not_say that given a pause you will have a change of strategy. The main hypothesis says very sensibly that if in an interaction situation there are certain points where the participants have an opportunity to evaluate the previous interaction, and are given feedback on their pers fOrmance, that is the most likely position for a Change in strategy to occur. However, there is a fUrther interesting question that can be asked of the data. Given that a strategy is occurring, what is the likelihood of a Change if a pause is introduced? If, under this con- dition, a pause does make a difference, more than would be expected by chance, i.e., with no pause occurring, this would be additional evidence that the evaluation period is a tool worth.manipulating to affect the outcomes of cooperation and competition.in bargaining situations. If under this extended test, the pause did not nake.a.significant differ- ence, it would suggest that although the presence of a strategy may be a good indicator in the absence of other information, it is not a vari- able worth nanipulating directly. Certain problems arise in testing the proposition: A pause significantly increases-the probability of a change in strategy. The problem is to establish a probability estimate, or Chance expectation. An estinate of p = .50 is not convincing as an estimate since in PDG we know that moves are not independent. Thus, the length of the stra- tegy would influence the probability of its changing. The best solution, 59 given the limitations of evidence, is to compute the a posteriori prob— ability across ali_strategy changes, regardless of where they occur, for strategies of different lengths, and then compare the number of ob- tained strategy changes to the number of non-changes for the first move as compared to the overall probability. Results are shown in Table 2. This second test differs from the main.hypothesis in that it in- cludes the number of times a strategy did not_change as well as the instances where it did. For example, it is possible in the first hy- pothesis that there were more opportunities for strategy changes, and thus a corresponding higher'number of Changes. One needs to look to see whether the higher number of Changes was due to more opportunities or to some effect of the evaluation pause. Since Changes of strategy cannot be manipulated, the experimenter is dependent on decisions of the players to establish his N. As seen in Table 2-1, the frequencies of strategies of different lengths is un- equally divided. Some of the categories are too small to make any meaninngl statement with the X2 statistic. Strategies of length six to nine are discounted on this ground. They are included in Table 2 to indicate that they mirror in miniature the effects f0und with the more frequent categories. Categories were decided in terms of the earlier definition of strategy. It was considered that once the number of consecutive moves reaChed ten, that differences of one move would not be significant, and the strategies were collapsed into five move categories. .All strategies over twenty consecutive moves long were considered locked-in, although strictly speaking this was not true. Nine out of 60 Table 2-1. Transition probabilities for strategies of different lengths across ail_moves. Strategy: Length u = 100/290 = .3H5 Strategy: Length 5 = H8/190 = .253 Strategy: Length 5 = 33/u2 = .232 Strategy: Length 7 = 18/109 = .155 Strategy: Length 8 = l9/9l = .209 Strategy: Length 9 = 8/72 = .110 Strategy: Length 10-14 = l9/6H = .297 Strategy: Length 15-19 = l7/H5 = .378 Table 2-2. Chi—square for obtained frequency of strategy changes on move one. 7 H 8 6 3.79 7.21 2.78 11.22 Length H (MOve One) Length 5 7 2 7 1 Length 10—1u Length 15—19 Strategy Length H (Move One): X2 = (7 — 3.79 - .5)2 + (H-7.2l-.5)2 3.79 +7.21 2.98 P < .10 61 Table 2-2 (contd). Chi—square for obtained frequency of strategy changes on move one. Strategy Length 5 (Move One): X2 = (8-2.78—.5)2 + (5-11.22-.5)2 2.78 11.22 = 9.86 P (.01 Strategy Length 6: 2 Changes/6 non-change .25 (.232 overall) Strategy Length 7: l change/2 non-Change .333 (.165 across all moves) Strategy Length 8: 4 changes/l non-change .80 (.209 across all moves) Strategy Length 9: 3 Changes/2 non-Changes = .60 (.110) Strategy Length 10—14: x2 = (7-.257-.5)2 + (2.5.33-.5)2 [l ““2757"" 5.33 ; 7.8r P = < .01 Strategy Length 15-19: X2 (7-3-.5)2 + (1-5-.5)2 = 5.53 P =.< .02 "1?“‘ “5“"" sixty-seven times this would have been untrue. However, the decision to consider them.locked-in was made since it does not make muCh sense to compare them with other situations since they never change. The issue is not how often there is a strategy change at MOve One, but how often there is or is not a strategy change there as compared to other moves where the strategy did eventually change. The significant of these frither tests (Table 2) gives prelrn- inary support to the potency of the pause in changing strategies. The pause not only signaled the most likely position for Changes in strategy to occur, but also has an effect in determining the probability of a Change given an occurring strategy. The size of the expected values in the X2 statistic should be increased to lend more weight to the findings. 62 Summary, More changes occur after a pause and feedback than at any other position in the sequence. A pause significantly increases the probability of a change in strategy for strategies of length four, five, ten- twenty, with preliminary evidence indicating that strategies of length six to nine follow the same pattern. Further testing of the effect of the pause and the communications concerning results should be done with larger samples where more in- stances of strategies occur. Necessary limitations of the definition and method of observation of strategies prevent the examination of the effect of the communication break in every instance. Often at the end of the 25th move, there was no formal strategy in evidence, and thus there was no way to gauge the first move of the next sequence as con- sistent or inconsistent with earlier decisions. This prevented the consideration of "conditional" strategy Changes (Martin, 1965). Never— theless, despite these shortcomings, the effect of the pause still af4 fected the course of the decision-making in Prisoner's Dilemma Game. It is possible that two facets of the intervention are important. The first would be the mere presence of a break in the decision—making sequence, and an opportunity to evaluate the course of the interaction. In this interval, some nanner of internal re-programming and considera- tion of feedback presumably occurs, mirroring internally the type of discussion recorded by Martin (196”) when the intervals were shared ‘with members of a team. Whether this evaluation can be measured without disturbing the interaction generated within the pair is a methodological problem that needs to be considered in later studies. The second 63 variable within the pause are the comrmmications addressed to the person concerning his own profits or losses, and those of his partner. It may stimulate comparison and consideration of outcomes that is not possible in the more rapid progression of Choices on the other twenty- four moves. The significance of the results bear on internal issues in Prisoner's Dilemma Game. It indicates that the simulation is not a con- tinuous sequence of equally important decisions. The interaction has been shaped by certain.crmmmnication inputs and the methodological pre- sentation of a pause after every twenty-five moves. Rapoport has been interested in tracing the course of the game fOr differentiating the overall results and it would seem profitable to recall that the pause changes the directions of the game. The results also lend evidence to the argument for PDG reflecting Choice behavior and not merely random behavior. It does suggest the equal.importance of decisions throughout the interaction is in question. Reservations concerning the results of the first hypothesis stem mainly from.the absence of a control group where subjects play without pause or feedbaCk. It seems very unlikely that in undifferentiated moves the 26th, Slst...276th trials would consistently differ. What is more likely and should be considered, is that part of the influence of the evaluation pause may be due to a contrast effect. If there were mere pauses, they would perhaps have less effect. However, it can be argued that they would have more effect on the likelihood of unfavorable outcomes being Changed. It may also be that the pause differentially effect changes from certain kinds of strategies to certain kinds of new 64 strategies. This will be discussed more fully in the final chapter. Hypothesis Two. The most frequent response type (CC, CD/DC, DD) in moves 6—10 predicts behavior for the remainder of the 25 move se— quence significantly more often than does prediction after the first five moves. f(Pr 6-10) > f (Pr 1-5) Null Hypothesis: There is no difference in the number of successful predictions in predicting from.moves 6-10 than prediction after moves 1—5. f (Pr 6-10) = f (Pr 1-5) Table 3 indicates that the hypothesis was not supported. There is no significant increase in predictive power in the second five trials as compared with the first five. Both sequences show a measure of ac- curacy that indicates some consistent influence throughout the game. There is a relation between the first ten moves and the remainder of that sequence. This is to be expected, since in a process model of communication and decision-making, all elements have some effect on subsequent behaviors. The proportion of right predictions is not very startling. It is useful to notice that the viability of CD or DC combinations (Prediction Type One) over time is not always reduced as Rapoport had suggested. The "unstable" combinations did not disappear into one of the two endstates, and predictions that unilateral endpoints would occur were not significantly different from.Prediction Two whiCh used only the stable states (CC or DD) as predictors. However, this result may be influenced unduly by the predominance of DC/CD Choices in the 65 Canadian pairs whiCh is not typical of most PDG outcomes. There is a continuing influence throughout the sequence and the slightly higher predictive power of the 6-10 trial block confirms the notion that the closer the move the more influence it has. (See Fig. 3) However, the increase from l-5 to 6-10 is not a Significant one and pro— vides no support for the belief that a "hardening" of strategies occurs shortly after the pause. This failure may be attributed to a non- occurrence of a strategy, or to a different rate of hardening, or to the fact that "hardening" does not occur at all. fhrther testing of this idea.might better~wait until measuring techniques are available and a better connection between behavior and.motivation establiShed for PDG in general. Table 3. Predictive power of trial block 6—10 vs. trial block l-5 (using all predictions (predictor one)). 5-10 Right 5—10 wrong (a) Both Right 1-5 wrong 1—5 Right Both wrong 87 56 47 65 x2 = (55 -51.5)2 + (47 —51.5>2 = .78 mpg, ““5I75‘ ““5I75‘ df = 1 6-10 % correct = 56% correct 1-5 % correct = 52.5% correct Predictive power of trial block 6—10 vs. trial block 1-5 (using Rapoport's indicators,(predictor two)). 6-10 Right 6-10 wrong (b) Both Right 1-5 wrong, 1—5 Right Both wropg 132 24 15 84 df = l X = (24 -19.5) + (15 -l9.5) = 2.08 N.S. 19.5 19.5 % correct. 6-10 = 61% correct 1—5 = 57% correct 66 Canadian—FrenCh Results Statistics as outlined in Chapter II will be reported, with the exception of the stoChastic indices whiCh are used to estimate trans- ition probabilities based on large numbers of subjects. Initial come parison with data collected in the United States by Rapoport and Chammah (1965) will be made at the end of the Chapter. (See Table 8) Table 4 lists the comparisons of the two samples. Those listed with an asterisk indicate significant differences equal to or greater than p. g .05 level. Statistic C, WhiCh is calculated by adding the average total number of paired cooperative moves (CC) per pair to the average number of unilateral cooperative responses (CD = DC/2) designates the overall level of cooperation of the nationality groupings. The proportions in the Table are Obtained by dividing the raw scores by three, although raw scores were used to calculate the tests for significant differences between them. Table 4. Comparison of Canadian and french samples. C CC CD/DC* DD C1 C2 Lcc/de* P.o Canadian .462 .258 .357 .385 .5 .5 .25 .275 french .53 .359 .225 .416 .464 .464 .714 .594 A t-test comparing the overall level of cooperation between the two samples indicates a non-significant difference. (See Table 5) Both samples aChieved a level of cooperation of approximately .50. 67 Table 5. t-test for Significance on overall outcomes (with raw scores). t = X1 ' X2 at = 28 (15 + 14—2) SD2 (1. + 1_) N1 N2 (a) Overall C (C + (CD+DC/2)) *4 t = 159 — 138.5 = .31 N.S. 1///5050 (l. + l.) ‘ 15 14 ; (b) t-test for CC t = 108 - 77 = 94 N.S df = 28 "““"' /8052 (1_ + 1_) y// 15 14 (c) t-test for (CD + DC) t = 107.2 - 67.6 = 2.256 ~/// 2304 (i_ +.1 16 14 P < .02 (2 tailed) (d) t—test for DD df - 28 t = 124.8 — 115.5 = .33 N.S. .//// 5210 (1. + 1.) 15 14 68 These findings do not contradict any earlier results from studies in United States. In almost all cooperative/competitive simulation games, only three conditions produced greater than .59 cooperative results. DeutsCh (1960) who told subject the goal of the game was cooperation; Oskamp and Perlman (1965) who explained the game beforehand, although not suggesting what the object of the game Should be; and Martin (1964) f who played PDG with teams and allowed intraeteamlcrmmunication at f evaluation pauses, were the only instances of greater than .59 coopera— E tion. Thus, the outcomes of the present samples do not seem.to differ 4 from past U.S. results. However, since the C statistic, is composed of two elements, the mutual cooperatives (CC) and the unilateral cooperations, the elements were fUrther broken down and t-tests performed on the CC re- sults, and the CD/DC results. Statistic EC, measuring the overall.mutual number of cooperative Choices, when compared by means of a t-test, is not significantly dif- ferent from.samp1e to sample. This would suggest that on the basis of the collected evidence, the ability of one nationality to reaCh a co- operative solution does not differ from the other. Statistic CD/DC, measuring the instances where one person Chose "l" (the cooperative move) while the other Chose "2" (the competitive move), does indicate a significant difference at the p = .02 level when compared by means of the t—test. This suggests that the Canadian sample pairs were less stable in reaching endpoints where both shared the profit (CC) or loss (DD). This is an unexpected finding since the pressures presumed to operate in PDG mitigate against an uneven result. 69 PUrther evidence bearing upon this finding will be discussed in the light of the LCC/LDD statistic. Statistic DD_comparing the number of mutually competitive moves, across samples, by means of the t-test, also revealed a non-significant difference. These four categories represent the summed tendencies of an "average" pair over 300 trials, rather than the endpoints of the inter- action. The results indicate that the main difference between the two samples is not a difference in competition or cooperation, but in the high number of unilateral moves in the Canadian sample. This finding has not been reported in any earlier studies. Usually the pair ends up in a state of CC or DD since it is unprofitable for one person to take a loss while the other gains at his expense. Table 9, as shown on page 85, outlines the large within-sample variance in all categories. This may be masking meaningful differences between the Canadian.and French samples. Both samples recorded large variances but an fLmax-test revealed no significant between sample vari— ance differences. However, by looking at Figs. 6, 7, and 8 one can see that there are distribution dissimilarities. The FrenCh sample seems to be highly bi-modal in CC and DD categories, either reaching high c00peration or high competition, while the Canadian sample is more prone to have uni- lateral strategies and.a.midd1e-range conclusion of cooperation or come petition. If the distributions are compared with a Kolmorgorov-Smirnov two sample test, the CD/DC distribution is the only one to reveal sig— nificant differences. It was significant at the p. g .02 level. See Table 5—2 for results of these tests. 70 oH mH :H mH NH . moHcEmm 05. 996 QOHHEHHBmHo HH OH m m m o boa/ca oo .55 .aaa 71 .moHcamm OE mmgom COHpanfimHo 00 mo scram 8mm .8 .MHM when 8888 Bane enema HmmjmosmmoHHHNHmHmeHonHmHNHHHonmmom:mmH III. I] om oo om OS fil a: l .1... 8H 1 , 3N _ .. ea .IuL C DE oom 72 .oHoEmm mo mo>oE 89 + Bo mo cacao nHom oH mH :H mH NH HH 0H m m s o m .na are om om om omH omH omH oHN ij osm oom 856 “Ho 2 73 oH mH :H mH NH HH 0H m w (bl o m.la m .m H .moHcEmm 039 mwooom m>oE oo\oo mo carom 9mm .os .MHM :H mH NH. HH 0H o m. b. o m a m N H when 8888 mnHmm cocoom cm or om QNH omH omH oHN o:N .nHoo he mocosomhe on Mo scram arm .om .mflm oH mH :H mH NH HH .bH m m s o m a m .m H :H mH mH HHl OH m m e m m a m N .H ......L..IIL..IIO om _IIAIII om rllulr. ONH Flrllu omH rl_ iii are i. TLIII 3N ,IILII ea osN oom 74 .oHcamm mo mo>oE om mo coupe .Mm .MHm mH mH :H mH NH HH 0H m m s m m a m N H om om om ONH omH omH OHN o:N osN oom 75 Table 5-2. Kolmogorov—Smirnov test to compare distributions. CC Distribution .3127 (a) D Max = [Snl (X) - Sn2 (X2)1 X2 4D2 nlnz n1 + n2 df = 2 _ 4(.3127)2 224 = 2.91 n.s. 14$15 ><1 N I (CD + DC) Distribution ; (b) D Max = .552 4 (.553)2 224 = 9.01 “30 X2 DD Distribution (c) D Max = .3127 X2 = 4 (.3127) 224 = 2.91 n.s. '30' Statistic LCC/LDD verifies this observation. The statistic in- dicates the number (percentage) of pairs where the last 25 trials were locked in on one behavior or the other. "Locked in" required that 22/25 of the last twenty-five trials be of the same paired behavior. Table 6 indicates, that, as would be expected from the earlier analysis, there was a significant difference at the p..{ 02 level between the 76 samples. Table 6. "Lock-in's" compared between samples. C 4 12 7.46 8.54 F 10 4 6.54 7.46 Canadian: 4/16 - .25 French: 10/14 = .714 x2 = (gig)? + (£13) + (_3._45>2 + (1.52)? = 5.4 7.46 6.54 8.54 7.46 df = 1 P < .02 It is the Canadian sample that deviates from what past results in PDG would suggest, while the FrenCh sample is quite similar to previous American outcomes. (See Rapoport data in Table 8.) P (0) represents the correlation between moves across the pairs. The formula for the correlation was taken from.Prisoner's Dilemma (Rapoport and Chammah, 1965) and represents the extent to which one subject's choice matCh the other's on the same trial. It is possible to estimate the significance of the difference between the two correla— tions. (Table 7) The statistics Cl and C2 reflect the proportion of subjects "W’ .209; m- :w' -. -L... ’ a. 77 Table 7. P (o) as compared across samples. Canadian P (o) = (CC) (DD) - (DC) (CD) = .2745 (CC+DD) (CC+DC) (DD+CD) (DD+DC) FrenCh P (o) = .5944 (CC) (DD) - (DC) (CD) (CC+CD) (CC+DC) (DD+CD) (DD+DC) = .5944 Fisher t-test for transferred r's t: Z1‘22 ‘ _1_+_1_ ‘ nl-3 112__3 t = .585 — 2.85 _ 94 n S .l_+ _1_ 13 ll (versus pair analysis in the other statistics) from the sample who Chose cooperatively on the first move. No test for significance was performed since it seemed obvious that there was no difference between the samples. (See Table 4) There seemed to be no noticeable differ- ence in initial tendencies of the pOpulations towards cooperation or competition, and that the end results were a function of the 223237 agtign generated within the process rather than external predisposi- ‘tions brought to the situation. Fig. 9 traces the process over time sequences of 15 trials. There does not seem.to be evidence of learning in the sequence for either sample. The Canadian sample began with an average cooperative proportion of .47 and finished.with an average cooperative proportion 78 Table 8. Rapoport U.S. data compared to French and Canadian with male-male, female-female breakdown. U.S- Rapoport 0 cc CD/DC DD 01 c2 LCC/LDD P.o n(70)MM .59 .51 .17 .32 .53 .48 .80 .45 n (70) PF .34 .23 .22 .55 .53 .49 .47 .31 French n (7) MM .41 .28 .26 .46 .22 .43 .43 .476 n (7) PF .53 .43 .19 .37 .71 .50 .86 .611 Canadian n (12) MM .46 .30 .32 .38 .50 .37 .4 .357 n ( 4) PF .37 .13 .46 .41 .50 .50 .87 of .434. The fluctuations during the process vary from .32 to .487. There does not seem to have been a learning process occurring as Rapoport has discussed. He has suggested (Chapter III, Prisoner's Dilemma) that there is a downward tendency after the first few trials, followed by a recovery about the 100—150 trial level, reaChing an asymptotic level of cooperation of about .60 shortly after the 150 trial level. The FrenCh sample appears to have shown an increase in coopera- tive behavior over time, although very slight. Cooperation began at the .455 level and increased to the .495 level, with cooperative levels varying from .367 to .559. As noted in Figs. 5 and 7 the FrenCh dis— tribution is heavily bi—modal and thus these "average pair" breakdowns do not reflect what is happening in the process. 79 —-———- Canadian French 80 70 10 008‘98Z SBZ'OLZ OLZ'SSZ SSZ‘OhZ OhZ‘SZZ SZZ‘OIZ 0IZ'96I 96I—08I 08I'99I 99I‘09I OSI‘GSI SST-OZI OZI‘SOI SOT-06 06 'SL SL ‘09 09 ‘Sfi 9h '08 08 'SI SI ‘0 Time course of C statistic across 300 trials. Fig. 9. jeans! 80 If Fig. 9 is compared with the same graph report from Rapoport's study (see Fig. 10), one can see the "recovery" factor whiCh in Rapoport's results holds for all three of his sub-samples, but is not present in the present samples, particularly the Canadian sample. Presumably, if the male—male, and female-female pairs were collapsed I to one sample summary, as is done in the present study, the overall proportion of cooperative behaviors would drop, but the sequence would remain the same. It may also be possible that the fact that both male—male and female-female pairs are included in the present samples may be dis- torting the patterns. However, although sample sizes of male—male and female-female are small when broken down in the French.and Canadian in- stances, Table 8 indicates (French sample) that the tendency seems to be the opposite of what occurred in the United States' sample. The French female pairs were more cooperative than the males, contrary to the Rapoport results where the male-male pairs were significantly more cooperative. Thus, if sex is having an effect in this particular sample, it is opposite to that whiCh would be expected. Summary} Neither~French nor Canadian samples reached a high level of cooperation. The samples differed on their tendency to lock—in on CC or DD behavior. The French sample was bi- modal, either highly CC or DD, while the Canadian subjects were strongly unilateral, not reaChing mutual solutions. In summarizing the comparison of the two samples, it is impor— tant to note that reservations over control abilities restrict con- clusions concerning the main effect of nationality (culture) on the 81 .memo pnomoomm no mo omnsoo QEHH .OH .me onsmm sssssss mnHom CHM: octz N Poomoom IIIIIII N #oomosm IIIIIII msHmm mnHmm a 8533 manner a 85.38 was H835, mHm>ooHCH monacmCVMHm o>Hmmoooom wcacooHso>oucoz Hopcostom 7. 7U 70 7e 7. 7. T. T. T. T. T. T. T. 8 L C4..." 7v T. 6 00 9 C4 00 7v 0 6 l.— 9 .n. 00 TL 9 _.L 9 TL 9 TL 9 TL 9 TL 9 T... 9 _.L 9 T. 9 TL 9 T. aararrarrtrrrt______ 0 8 /.. C4 h. 3 TL 6 8 9 C4 00 7V 0 6 L 9 .fi. 00 TL 0 C4 0 C4 0 C4 0 C4 0 C4 0 C4 0 C4 0 C4 0 C4 0 C4 when Smear oH ON om o: om mQHom omxflz or on om 82 playing of Prisoner's Dilemma. A potentially disruptive factor in the sample is the fact that the French subjects knew eaCh other befOre taking part in the experiment, and thus differences may be attributable to differences in cooperative behavior between friends and non-friends. However, there is some evidence that this did not influence the dif- ferences. First of all, friendship did not seem.to lead to a.higher level of cooperation as the expectation might have been, but resulted ' in a bi-modal outcome: highly cooperative or highly competitive. Five of the French pairs were highly cooperative; seven of the FrenCh pairs were highly competitive. The difference that was revealed between the two samples is largely due to the high unilateral moves by the Canadian pairs. A.look at the Rapoport data (Table 8) indicates that the French breakdown of categories was quite similar to the United States' sample. Another study conducted in the U.S. (Oskamp and Perlman, 1965) showed that the degree of friendship between the subjects had no effect on the level of cooperation, at least within the range from."unacquainted" to "fairly friendly." However, that researCh did not investigate the ex- tremes of very good friendship and dislike, and these extreme positions may affect cooperation. In the present study, the FrenCh group had been together for six to eight weeks, and it is difficult to estimate what level of friendship should be ascribed to them. They were assigned randomly to pairs, but this could not overcome the interaction effect of traveling in the same party. If friendship had an effect, it was not consistent, and can probably be discounted. An additional complication is the non-similar composition of the samples in regard to sex. Twelve of sixteen Canadian pairs were male; re p... A. .b,.~.,|. 83 seven of fourteen were male in the FrenCh sample. Earlier studies by Lutzker (1961) and Oskamp and Perlman (1965) testing 210 pairs of sub- ject, and employing the 300 trial sequence did find differences. The comparison with Rapoport's data on United States' students can be done with some certainty with the male and female French pairs, and the male Canadian sub-sample. The number of female pairs (4) in the Canadian sample seems too small for'a legitimate comparison. An interesting difference (see Table 8) is the reversal of the level of cooperation and competition between male-male and female-female pairs between FrenCh and American subjects. Where for the U.S. sample, the males were significantly more cooperative, there was no significant difference between the male and female French pairs. The tendency was for the females to be more cooperative. Rapoport does not indicate in his data.whether the results of this particular comparison were in fact significant, but with a sample size of 140 it seems that .57 and .34 are statistically significant at a high level of reliability. The FrenCh sample was based on a much smaller number, and thus the former findings are probably more reliable. However, the effect of the vari- able, sex, was not significant in comparing the FrenCh and Canadian samples. The major obstruction to reliable inferences between the samples is the size of the samples. The greater similarities between the FrenCh and Canadian samples with regard to the overall level of cooperation and progress towards cooperation seemlsuspicious, and should be tested fUrther'within a larger framework, but not probably as a separate in— quiry since the United States' findings themselves are not consistent across experiments. 84 Chapter Summary Two hypotheses were examined. The first dealt with the impor- tance of the evaluation pause and the communications concerning results during that pause in increasing the probability of a strategy Change. Results from a X2 test (Table 1) indicated that the pause did have a Significant value as a predictor of where a strategy change was most likely to occur, and in a.more specific test, was significant with stra- tegies of different lengths, in increasing the likelihood of a strategy Change, given that a strategy was occurring. The second hypothesis, suggesting that the second five moves in the 25 move sequence between pauses were significantly better predictors of the final outcomes of that sequence, was not confirmed. One could take the predictions at the end of the first five moves and make equally . good (statistically) predictions. The tenuousness of the hypothesis is evident, and was intended as a minor investigation into the question of the importance of different segments in making strategy decisions. The third area that was considered was the comparison of FrenCh and Canadian samples as distinct populations to be compared. The Canadian sample was found to consistently perform more unilateral be- haviors, although overall cooperation or competition by either sample did not differ significantly from each other,* nor reaCh a greater level of cooperation than most previous studies with.American college students. *A.breakdown into nationality in terms of the first hypothesis, that is, the occurrence of strategy changes showed no distinct difference. Of 290 strategy Changes, 155 occurred in the French sample, 135 in the Canadian. The effect of the pairs did not appear to vary between samples, 25/155 occurring in the first move in the FrenCh sample and 23/135 occurring in the Canadian. There was no interaction effect 85 Table 9. Within-group variance of nationality samples. Variance = N( X2) - ( X)2 (N) (N—1)7 Canadian (61) C X: 138.6 Y?- 67.6 V = 3,416 V = 1,205 SD = 58.5 SD = 34 (b) CC X = 84.5 X = 107.5 v = 5,558 v = 10,919 SD = V = 74.5 SD = V = 104.3 (c) CD/DC SE: 104 Y: 57.5 v = 1,719 v = 1,205 SD = 41.5 SD : 3H (d) DD 2 = 115 Y = 124.8 v = 3,039 v = 7,714 SD = 54.8 SD = 87.9 with the pause and nationality. CHAPTER IV CONCLUSIONS The main interests of the study were to explore the internal mechanisms of the PDG game as a communication, decision—making simula- tion, and more specifically, to hypothesize that communications intro- duced during an evaluation pause following each segment of twenty-five moves was a variable that affects decisions to cooperate or compete. { In earlier studies, Rapoport (1965) had begun to break down the Ll model of cooperation into a process that developed over 300 moves, and ? hoped to outline certain points that were most important fOr this de— cision—making situation. The present consideration of the pause and the communication feedback involved in the instructions was a first step in exploring these particular decision "nodes." Results indicate that the first move in a sequence was significantly higher in Changes of strategies. than any other move, and results of significance were obtained with strategies of different lengths where the evaluation pause Changed the course of interaction. Changes of strategy were measured by observing the behavior on the first move following a pause. One of the difficulties in testing the hypothesis is that strategies cannot be simulated and that the fre- quency of their occurrence cannot be manipulated. In the present ex- periment, it would.have been useful if more strategy Changes had occurred after the pause in order to break down the Changes into the direction of the change, and the nature of the strategy that was Changed. If the internal variables of the model were going to be ex- 86 87 plored, the researCh suggestion stemming from this study would be to conduct the study with a larger~N, and sub—divide the strategies into categories (CC, (313/ DC, DD). Changes towards greater cooperation would be the interest of this experimenter and it would be useful to know whether the pause is more productive of cooperative rather than compet- . itive Changes. Martin (1964) found that the pause in groups of three team members and.crnmunication allowed them, significantly increased cooperation. The present study, although discussing strategy Changes in . general, does suggest that discussion of the process of learning co- operation over 300 trials should take into account the fact that the methodological intervention of feedback concerning recent performance, and time to evaluate past behavior, is affecting the course of the inters action, and the situation is not_simply two people interacting together in azmixedamotive situation. In this instance, communications from.the experimenter are having an effect. It might suggest that the 25 trial sequence is a better unit to use in comparing progress of cooperation over time than the 15 trial breakdown by Rapoport. Finally, it should be remembered that the purpose of the study was to test these internal questions as well as make preliminary inves— tigations of nationality differences. Although the data.was collected from both FrenCh and Canadian pairs, it was not likely that there was any correlation between nationality and Changes of strategies. It may be that the frequency of strategy Changes was curtailed in the Canadian sample because of the smaller number of mutual choices (Fig. 6), but this should not have biased the testing of the hypothesis concerning 88 the importance of the first move. The addition of the second hypothesis stemmed.from.the theory that if a strategy Change is likely to occur after a pause, it depends upon a response from.the other player for its continuance. The first few moves would be trial moves to see if the strategy is mutually ac- ceptable. If it is, then by the 10th.move, the general pattern for the remainder of the sequence Should be established. If it is not, then the pair should revert to some acceptable form fairly quickly, and like— wise be "hardened" by the 10th move. The hypothesis was not confirmed, and could be examined more precisely in an experiment concerning pauses where it is possible to examine reactions to strategy Changes by col- lecting questionnaire data. Without this, there does not seem to be any way of telling what motivations underlie the present non-significant results. For example, it may have been the case that no strategy occurred on the first move, or that the behavior hardened.much.earlier than the 10 trial level, or that pair analysis obscured individual reactions to stra- tegy Changes. It does not seemlworth pursuing to any depth on its own merits. The third area of exploration, and what initially was to be the kernel of the study, was the effect of nationality on the playing of PDG. It seemed possible that with radically different cultural backgrounds there might be different sets towards cooperation and different methods of interaction in establishing outcomes. With the FrenCh and Canadian samples, there was not the same element of "obvious" cultural difference. However, the process of cooperation did differ in the method of reaChing endpoints. The Canadian sample seemed to vacillate between C and D .5. 314'. I 0» Kit} 89 moves, and made a significantly greater number of unilateral moves (CD/DC) moves than the FrenCh sample and the earlier study by Rapoport and Chammah.(1965). Neither sample reaChed a high level of cooperation. It would seem worthwhile to explore the Canadian findings by extending the testing to other subjects to find out what might lie behind this phenomenon. It contradicts what is plausible in discussions of the pressures operating in the game. m Further internal examination of PDG should be made to understand the positions that represent key decision points. Moves immediately following the pauses were found significant, and should be examined to see whether they have a differential effect on the kind of Change that occurs. Further consideration of PDG as a rudimentary model of a pom: munication process should reveal valuable hypotheses for testing. Nationality as variable in cooperative/competitive simulations needs testing. It is hoped that an extension of this study would in- clude some non-Western nationalities. APPENDICES ,7 APPENDIX A PAIR CHARACTERISTICS French Age Education Sex DBF #1 .A 20 14 yrs. F B 17 11 yrs. F DBF #2 A. 17 11 yrs. M B 17 11 yrs. M DBF #4 .A 17 11 yrs. M B 18 11 yrs. M DBF #6 A 17 11 yrs. M B 22 16 yrs. M DBF #5 .A 15 11 yrs. F ‘ B 22 15 yrs. F J DBF #10 .A 20 14 yrs. F B 22 8 yrs. F DBF #11 .A 18 10 yrs. M B 26 20 yrs. M DBF #12 A 17 11 yrs. F B 18 12 yrs. F DBF #13 .A 22 16 yrs. F B l9 13 yrs. F DBF #14 A. 21 15 yrs. M B 26 17 yrs. M DBF #9 A. l8 14 yrs. F B l7 12 yrs. F DBF #8 A 17 13 yrs. F B l8 14 yrs. F DBF #7 .A 20 13 yrs. M B 18 11 yrs. M DBF #3 .A 16 11 yrs. M B 20 14 yrs. M Average Age: 19.1 Average Yrs.: 12.8 91 92 Appendix A, (contd) PARTICIPANT CHARACTERISTICS Canadian Age Education Sex DBC #4 A 22 4 yrs. univ. M B 20 1 yr. univ. M DBC #18 A 27 4 yrs. univ. F B 21 4 yrs. univ. F DBC #2 A 23 15 yrs. ed. M B 26 M DBC #3 A 24 17 yrs. ed. M 4. B 25 M r DBC #17 A 21 11 yrs. school M f B 25 16 yrs. school M DBC #6 A 20 M B 27 M DBC #5 A 25 16 yrs. school M B 24 1 yr. masters M DBC #16 A 20 13 yrs. school F B 25 Gr. 11 F DBC #15 A 22 13 yrs. F B 31 11 yrs. F DBC #14 A 19 3 yrs. univ. M B 27 17 yrs. school M DBC #10 A 21 15 yrs. M B 24 15 yrs. M DBC #9 A 20 12 yrs. M B 26 2 yrs. univ. M DBC #7 A 22 13 yrs. M B 28 Masters (M.Sc.) DBC #19 A 23 4 yrs. univ. F B 33 11 1/2 yrs. F DBC #20 A 22 10 yrs. M B 32 B.Sc. M DBC #1 A M B M Average Age: 2L1, 2 Average Educ: 13.9 yrs. 93 DUNN \\\\ ——-— p..— —-—— m.:oH m.boN m.moH m.mmH m.owN moH :m smN QmLL-am mm mm m NNH so m: :N ooH on o m mH osN um 00 oH mm Anm>oe mm ante ea Aooo nauxooa n>aennmnooo Ann>oa mm arse ea Ammo nauxooa nsaraennaoo \\\\ .... QQNN \\\\ QUON Nu m.NoN m.Ns m.mh :mH ms mN NH mm mm wN muH 00 00 Q0 00 m o m m m m MD MD NmH om mm bN 8 amp—«(x mmmoom mH2= 900,501 Raw Scores DD STATISTIC ACROSS PAIRS: Canadian 25x 2ix2 ( X)2 115 128 170 111 108 139 25 34 131 70 55 215 189 55 155 141 1,847 258,805 3,411,409 98 APPENDIX C RAW SCORES FrenCh éi>< 21x2 ( X)2 264 168 169 171 182 73 184 67 95 257 103 1,747 318,279 3,052,009 BIBLIOGRAPHY . Bixenstein, V. E., Potash, H. K., 8 Wilson, K. V., "Effects of level of cooperative choice by the other player on choices in a prisoner' s dilemma game: Part 1," _tl. Abnorm. Soc. 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