Reciprocation of generosity and knowledge of game termination in the decomposed Prisoner's Dilemma Game

Sahlins proposed a model of reciprocity for social interaction citing three forms drawn from observations of kinship systems. The model describes an altruistic form of reciprocity, a balanced or economic form and a negative form in which individuals try to outdo each other. This model was applied to a two-person variation of the Prisoner's Dilemma Game where Ss were presented with a confederate who responded over trials entirely generously, contingently generously or non-generously. Half of the Ss were informed that there would be ten trials while the other half were uninformed. Basically, Ss tended to match the generosity level of the confederate and were less generous when trial number was known. Evidence for Sahlins' model is provided by Ss reports of reasons for their choices in the game. Those in the generous condition gave reasons for reciprocating based on a general feeling of obligation, trust and desire to cooperate. Those in the contingently generous condition gave reasons for reciprocating based on economic exchange and a desire to maintain a balance of resources. Ss in the non-generous condition gave reasons based on a desire to take what profits one could before the other got them. In addition, Ss indicated a significant tendency to exploit the other on the final trial under the informed condition for the contingently generous but not for the generous condition.     

Understanding cooperation in the Prisoner’s Dilemma game

In the standard one-shot Prisoner’s Dilemma game, participants often choose to cooperate, when the optimal strategy is to defect. This puzzling finding has attracted considerable interest both in terms of possible computational frameworks for modeling human judgment, but also regarding the more general debate of human altruism. In this research, we ask how much of human behavior in this task can be explained by a putative bias for cooperative behavior and whether this, in turn, is influenced by personality. We compared performance on the standard task with performance on a matched neutral one; we manipulated the optimal strategy (defect or cooperate); and we manipulated the amount of payoff for responding optimally. Results revealed little evidence for a bias for cooperative behavior, but significant associations with the personality factors of Behavioural Activation System (BAS) Reward Responsivity and Agreeableness were found. These findings are discussed in terms of the attempt to explain judgment in one-shot, Prisoner’s Dilemma tasks with statistical or probabilistic models.     

Co-operative solutions to the Prisoner's Dilemma

For helpful comments, my thanks to Robert Bright, Richmond Campbell, Julia Colterjohn, Peter Danielson, Ish Haji, Keith Lehrer, Robert Martin, Victoria McGeer, Terrence Tomkow and an anonymous referee. I also thank the Canadian S.S.H.R.C. for a Doctoral Fellowship and Dalhousie University for a Killam Post-Doctoral Fellowship.     

Self‐control in a Prisoner's Dilemma game: the role of trial spacing and an interfering task

Self‐control was studied in an iterated one‐player Prisoner's Dilemma game in which students' choices affected the payoff matrix on the next trial. The frequency of self‐control responses (choice of the smaller payoff now, but with the more generous payoff matrix more likely on the next trial) and defection responses (choice of the larger payoff now, but with the less generous payoff matrix more likely on the next trial) were measured. In Experiment 1, players achieved a criterion of five consecutive self‐control responses more quickly as a positive function of trial spacing, the presence between trials of a discriminative stimulus associated with the upcoming payoff matrix, and the probability that the self‐control or defection response would be reciprocated by the computer. Experiment 2 replicated the effect of trial spacing except when there was an interfering task during the interval, suggesting that trial spacing permits better appreciation of the contingencies. Copyright © 2006 John Wiley & Sons, Ltd.     

Reward, punishment, and cooperation: a meta-analysis

How effective are rewards (for cooperation) and punishment (for noncooperation) as tools to promote cooperation in social dilemmas or situations when immediate self-interest and longer term collective interest conflict? What variables can promote the impact of these incentives? Although such questions have been examined, social and behavioral scientists provide different answers. To date, there is no theoretical and/or quantitative review of rewards and punishments as incentives for cooperation in social dilemmas. Using a novel interdependence-theoretic framework, we propose that rewards and punishments should both promote cooperation, and we identify 2 variables—cost of incentives and source of incentives—that are predicted to magnify the effectiveness of these incentives in promoting cooperation.A meta-analysis involving 187 effect sizes revealed that rewards and punishments exhibited a statistically equivalent positive effect on cooperation (d =0.51 and 0.70, respectively). The effectiveness of incentives was stronger when the incentives were costly to administer, compared to free. Centralization of incentives did not moderate the effect size. Punishments were also more effective during iterated dilemmas when participants continued to interact in the same group, compared to both (a) iterated dilemmas with reassignment to a new group after each trial and (b) one-shot dilemmas. We also examine several other potential moderators, such as iterations, partner matching, group size, country, and participant payment. We discuss broad conclusions, consider implications for theory, and suggest directions for future research on rewards and punishment in social dilemmas.     

Behavioural Consistency Within the Prisoner's Dilemma Game: The Role of Personality and Situation

Mixed‐motive games represent situations that confront people with a conflict between cooperative and non‐cooperative alternatives. Despite this common basis, recent research has shown that the consistency of people's choices across different mixed‐motive games is rather low. The present research examined behavioural consistency within the same mixed‐motive game, by presenting participants with a series of one‐shot Prisoner's Dilemma Games. Across this set of games, payoffs were manipulated in order to intensify or weaken the conflict between self and the other party while maintaining the game's underlying structure. Our findings indicate that significant differences in choice behaviour are observed as a function of both situational (i.e. manipulations of the Prisoner's Dilemma Game's payoff structure) and personality differences (i.e. individual differences in personality and motivational traits). Moreover, our included situational variables and personality features did not interact with each other and were about equally impactful in shaping cooperation. Crucially, however, despite the significant behavioural differences across game variants, considerable consistency in choices was found as well, which suggests that the game's motivational basis reliably impacts choice behaviour in spite of situational and personality variations. We discuss implications for theorizing on mixed‐motive situations and elaborate on the question how cooperation can be promoted. © 2018 European Association of Personality Psychology     

Risk and Prisoner's Dilemma: A Reinterpretation of Coombs' Re‐parameterization

We propose a model to measure risk in a prisoner's dilemma based on Coombs' (1973) re‐parameterization of the game as an individual risk decision‐making task that chooses between a gamble of cooperation and another gamble of defection. Specifically, we propose an index, r, to represent the risk associated with cooperation relative to defection. In conjunction with Rapoport's (1967) index of cooperation (K), our formulation of risk allows us to construct games that vary in risk (as indexed by r) while controlling for cooperativeness (as indexed by K). Following utility analysis that models risk seeking as a convex utility function and risk averse as a concave function, we predict that risk‐seeking people cooperate more in games that the cooperation choice is more risky, whereas risk‐averse people cooperate more in games that the cooperation choice is less risky. In the three studies that we varied game parameters, used different measures of risk orientation and prosocial orientation and used different experimental procedures, we found robust results supporting our predictions. Theoretical analysis of our formulation further suggests that risk and cooperativeness of a prisoner's dilemma game is not entirely independent. Games that have a higher cooperativeness index are necessarily more risky. Copyright © 2011 John Wiley & Sons, Ltd.     

Encouraging Cooperation: Revisiting Solidarity and Commitment Effects in Prisoner's Dilemma Games1

Pre‐play discussion consistently increases cooperation in dilemma interactions. Most explanations of this “cheap‐talk” effect are based on either commitment or group solidarity effects. Because discussion about the upcoming dilemma allows participants to make promises and creates group solidarity, the 2 explanations are often confounded. This paper aims to clarify past results by having participants engage in an unrelated discussion prior to a dilemma interaction. We find that solidarity effects can be induced by minimal group categorizations, but are relatively weak. Discussions involving consequential but unrelated coordination tasks are shown to prime cooperative norms and increase cooperation with both in‐group and out‐group members. Our findings suggest that cheap talk may work for even cheaper reasons than previously thought.     

囚徒困境决策中分离效应验证性与机制研究

Savage于1954年提出"确定事件原则"这一概念,Tversky和Slafir(1992)通过实验发现,人们在不确定条件下的决策过程中,会出现违背确定事件原则的现象,并把这种现象称为"分离效应"。尽管已经有很多对于二次赌博中分离效应的机制研究并产生很多分歧,但对于囚徒困境范式中是否存在分离效应以及其机制并没有一致的结果。本文对囚徒困境中的分离效应进行了验证性实验,虽然整体结果上与Shafir与Tversky(1992)的结论相吻合,但被试专业背景对结果有显著效应。同时,按照Lambdin和Burdsal(2007)对分离效应的操作定义,结果发现分离效应没有出现,文章对其原因进行了讨论。     

Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game

Experimental games have previously been used to study principles of human interaction. Many such games are characterized by iterated or repeated designs that model dynamic relationships, including reciprocal cooperation. To enable the study of infinite game repetitions and to avoid endgame effects of lower cooperation toward the final game round, investigators have introduced random termination rules. This study extends previous research that has focused narrowly on repeated Prisoner's Dilemma games by conducting a controlled experiment of two‐player, random termination Centipede games involving probabilistic reinforcement and characterized by the longest decision sequences reported in the empirical literature to date (24 decision nodes). Specifically, we assessed mean exit points and cooperation rates, and compared the effects of four different termination rules: no random game termination, random game termination with constant termination probability, random game termination with increasing termination probability, and random game termination with decreasing termination probability. We found that although mean exit points were lower for games with shorter expected game lengths, the subjects' cooperativeness was significantly reduced only in the most extreme condition with decreasing computer termination probability and an expected game length of two decision nodes.     

Rationality and bounded information in repeated games, with application to the iterated Prisoner's Dilemma

Actions in a repeated game can in principle depend on all previous outcomes. Given this vast policy space, human players may often be forced to use heuristics that base actions on incomplete information, such as the outcomes of only the most recent trials. Here it is proven that such bounded rationality is often fully rational, in that the optimal policy based on some limited information about the game's history will be universally optimal (i.e., within the full policy space), provided that one's opponents are restricted to using this same information. It is then shown how this result allows explicit calculation of subgame-perfect equilibria (SPEs) for any repeated or stochastic game. The technique is applied to the iterated Prisoner's Dilemma for the case of 1-back memory. Two classes of SPEs are derived, which exhibit varying degrees of (individually rational) cooperation as a result of repeated interaction.