Classroom Games: A Prisoner's Dilemma

This survey of intermediate microeconomic textbooks will be helpful to those in the throes of selecting a suitable text. The author identifies the major review criteria and examines nine widely used books, grouping them by type of approach.     

Voluntarily Separable Repeated Prisoner's Dilemma

Ordinary repeated games do not apply to real societies where one can cheat and escape from partners. We formulate a model of endogenous relationships that a player can unilaterally end and start with a randomly assigned new partner with no information flow. Focusing on two-person, two-action Prisoner's Dilemma, we show that the endogenous duration of partnerships generates a significantly different evolutionary stability structure from ordinary random matching games. Monomorphic equilibria require initial trust building, while a polymorphic equilibrium includes earlier cooperators than any strategy in monomorphic equilibria and is thus more efficient. This is due to the non-linearity of average payoffs.     

A Folk Theorem for Repeated Sequential Games

We study repeated sequential games where players may not move simultaneously in stage games. We introduce the concept of effective minimax for sequential games and establish a Folk theorem for repeated sequential games. The Folk theorem asserts that any feasible payoff vector where every player receives more than his effective minimax value in a sequential stage game can be supported by a subgame perfect equilibrium in the corresponding repeated sequential game when players are sufficiently patient. The results of this paper generalize those of Wen (1994), and of Fudenberg and Maskin (1986). The model of repeated sequential games and the concept of effective minimax provide an alternative view to the Anti–Folk theorem of Lagunoff and Matsui (1997) for asynchronously repeated pure coordination games.     

In-class Simulations of the Iterated Prisoner's Dilemma Game

The author developed a simple computer program for the in-class simulation of the repeated prisoner's dilemma game with student-designed strategies. He describes the basic features of the software and presents two examples for the use of the program in teaching the problems of cooperation among profit-maximizing agents.     

The Repeated Prisoner's Dilemma with Imperfect Private Monitoring

In this paper, I study a repeated Prisoner's Dilemma game in which monitoring is private and imperfect. A partial folk theorem is proved for the case of almost perfect monitoring.     

The Sequential Prisoner's Dilemma: Evidence on Reciprocation

We investigate how fairness concerns influence individual behaviour in social dilemmas. Using a Sequential Prisoner's Dilemma experiment we analyse the extent to which co-operation is conditional on first-mover co-operation, repetition, economic incentives, subject pool (United Kingdom vs. United States) and gender. We find the most important variable influencing co-operation is the first-mover's choice, supporting the argument that co-operative behaviour in social dilemmas reflects reciprocation rather than unconditional altruism. However, we also find that co-operation decreases with repetition, and reciprocation falls as its material cost rises.     

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n  ≥  4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.” A previous version of this paper was circulated as Anderlini et al. (2005). We are grateful to Jeff Ely, Leonardo Felli, Navin Kartik, David Levine, Stephen Morris, Michele Piccione, Andrew Postlewaite, Lones Smith and to seminar audiences at Bocconi, Cambridge, CEPR-Guerzensee, Chicago, Columbia, Edinburgh, Essex, Georgetown, Leicester, LSE, Northwestern, Oxford, Rome (La Sapienza), Rutgers, SAET-Vigo, Stanford, SUNY-Albany, UCL, UC-San Diego, Venice and Yale for helpful feedback.     

When a Precedent of Donation Favors Defection in the Prisoner's Dilemma

Abstract. In this paper, we examine the question of whether a collective activity can influence cooperation in a subsequent repeated one‐shot prisoner's dilemma (PD) game. We conduct two series of experiments. The first consists of control experiments in which 30 periods of a PD game are played, with a random rematching of the pairs in every period. In a second series of experiments, subjects first play a donation game (DG) and then the PD game. In the DG, they collectively discuss the amount of a donation to a given charity, before putting the question to an individual and anonymous vote. Cooperation levels in the PD games preceded by the DG are significantly lower than those observed in the control experiment.     

End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach

A learning theory is proposed which models the influence of experience on end behavior in finite Prisoner's Dilemma supergames. The theory is compared with experimental results. In the experiment 35 subjects participated in 25 Prisoner's Dilemma supergames of ten periods each against anonymous opponents, changing from supergame to supergame. The typical behavior of experienced subjects involves cooperation until shortly before the end of the supergame. The theory explains shifts in the intended deviation period. On the basis of parameter estimates for each subject derived from the first 20 supergames, successful predictions could be obtained for the last five supergames.     

Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games

This paper investigates cooperative play in prisoner's dilemma games by designing an experiment to evaluate the ability of two leading theories of observed cooperation: reputation building and altruism. We analyze both one-shot and finitely repeated games to gauge the importance of these theories. We conclude that neither altruism nor reputation building alone can explain our observations. The reputation model is inconsistent with play in both one-shots and finitely repeated games while the model with altruism is unable to explain observed play in the finitely repeated games.Journal of Economic LiteratureClassification Numbers: C72, C92.     

防范国企经营者合谋：不对称信息的“囚徒困境”博弈

如何防范国企经营者和主管部门官员之间合谋侵占国有企业的生产剩余,一直是政府部门和学术界关注的焦点问题。本文根据Laffont和Martimort等在委托-代理框架下提出的分权制思想,构建了防范国企经营者合谋的"囚徒困境"博弈模型。但由于基于"囚徒困境"博弈所构建的双重审核机制可能产生过高的审查成本,且其实施受到主管官员有限责任的限制,因此通过引入不对称信息进一步改进了"囚徒困境"博弈,使不合谋的均衡结果能在更宽松的条件下实现。     

Expectations in Austrian Business Cycle Theory: An Application of the Prisoner's Dilemma

The standard account of Austrian Business Cycle theory posits that central bank manipulations of interest rates fool bankers and investors into believing that there has been an increase in the real supply of loanable funds available for capital investment. However, reliance on foolishness ignores the entrepreneurial emphasis within the Austrian tradition and fails to produce the strongest possible case for Austrian Business Cycle theory. We use the prisoner's dilemma framework to model the profit maximizing behavior of bankers and the investors under uncertainty when the market rate of interest is below the underlying rate of time preference.     

从"囚徒困境"看大都市圈经济整合

大都市圈经济整合是大都市圈发展的关键环节,是大都市圈功能的具体反映.通过对大都市圈经济整合中的"囚徒困境"分析,得出了中国大都市圈经济整合中所产生的"囚徒困境"是制度缺陷造成的.因此,破解"囚徒困境"的方法就是寻求制度创新.     

Endogenous transfers in the Prisoner's Dilemma game: An experimental test of cooperation and coordination

We test a two-stage compensation mechanism for promoting cooperation in Prisoner's Dilemma games. Players first simultaneously choose binding non-negative amounts to pay their counterparts for cooperating, and then play the induced game knowing these amounts. In our games, all payment pairs consistent with mutual cooperation in subgame-perfect equilibrium transform these games into coordination games, with both mutual cooperation and mutual defection as Nash equilibria in the second stage. When endogenous transfer payments are not permitted, cooperation is much less likely. Mutual cooperation is most likely when the (sufficient) payments are identical, and it is also substantially more likely with payment pairs that bring the mutual-cooperation payoffs closer together. Both the Fehr–Schmidt and Charness–Rabin models predict that transfers that make final payoffs closer are preferred; however, they do not explain why equal transfers are particularly effective. Transfers are also effective in sustaining cooperation even when they are imposed and not chosen.     

Nonparametric Analysis of Longitudinal Binary Data: An Application to the Intergroup Prisoner's Dilemma Game

The intergroup prisoner's dilemma game was suggested by Bornstein (1992, Journal of Personality and Social Psychology. 7, 597–606) for modelling intergroup conflicts over continuous public goods. We analyse data of an experiment in which the game was played for 150 rounds, under three matching conditions. The objective is to study differences in the investment patterns of players in the different groups. A repeated measures analysis was conducted by Goren and Bornstein (1999, Games and Human Behaviour: Essays in Honor of Amnon Rapoport, pp. 299–314), involving data aggregation and strong distributional assumptions. Here we introduce a nonparametric approach based on permutation tests. Two new measures, the cumulative investment and the normalised cumulative investment, provide additional insight into the differences between groups. The proposed tests are based on the area under the investment curves. They identify an overall difference between the groups as well as pairwise differences. A simultaneous confidence band for the mean difference curve is used to detect the games which account for any pairwise difference.     

Folk Theorem For Bilateral Bargaining with Vector Endowments

We analyse a bargaining game of two players on the division of the sum of their vector endowments, with alternating proposals and discounting of single period utilities. The pair of endowments is not weakly Pareto‐efficient. Until they reach an agreement, each of the parties can withdraw from bargaining and keep their endowments. Any strictly individually rational division of the sum of endowments can emerge in some subgame perfect equilibrium if discount factors are close enough to one. Each subgame perfect equilibrium, in which the parties’ decisions do not depend on past rejected proposals, leads to a weakly Pareto‐efficient agreement in the first period.     

关于非齐次马氏链的一个强极限定理

应用鞅差序列的收敛定理给出可列非齐次马氏链系数的一个强极限定理,作为推论,得到了任意非齐次马氏链加权和的极限定理.     

金钱与自主--市民社会面临的两难境地

为什么市民社会总是无法达到其支持者的期望?这篇论文提供了一个解释:即缺乏独立于国家和企业之外的财务和运营自主权。本文表明,市民社会自给自足这一普遍深入人心的神话根本没有事实基础。实际上,私人慈善团体在任何一个国家都不可能成为市民社会组织的主导性收入来源。那么,什么才是呢?市民社会组织的收入来源在各个国家是否相同?资金来源如何影响它们的行为?在多大程度上,市民社会组织真的从国家和企业独立出来并获得了自主?这些都是本文试图回答的问题。