The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments

In the infinitely repeated Prisoners' Dilemma with side payments, we characterize the Pareto frontier of the set of subgame perfect equilibrium payoffs for all possible combinations of discount factors. Play paths implementing Pareto dominant equilibrium payoffs are uniquely determined in all but the first period. Full cooperation does not necessarily implement these payoffs even when it maximizes total stage game payoffs. Rather, when the difference in players' discount factors is sufficiently large, Pareto dominant equilibrium payoffs are implemented by partial cooperation supported by repeated payments from the impatient to the patient player. When both players are sufficiently patient, such payoffs, while implemented via full cooperation, are supported by repeated payments from the impatient to the patient player. We characterize conditions under which public randomization has no impact on the Pareto dominant equilibrium payoffs and conditions under which such payoffs are robust to renegotiation.     

Rational cooperation in the finitely repeated prisoners' dilemma

A common observation in experiments involving finite repetition of the prisoners' dilemma is that players do not always play the single-period dominant strategies (“finking”), but instead achieve some measure of cooperation. Yet finking at each stage is the only Nash equilibrium in the finitely repeated game. We show here how incomplete information about one or both players' options, motivation or behavior can explain the observed cooperation. Specifically, we provide a bound on the number of rounds at which Fink may be played, when one player may possibly be committed to a “Tit-for-Tat” strategy.     

Personality and cooperation in finitely repeated prisoner’s dilemma games

We investigate the role personality plays in Finitely Repeated Prisoner’s Dilemma (FRPD) games. Even after controlling for demographic factors such as race, course of study, and cognitive ability, we find that cooperative behavior is significantly related to the Big Five personality trait Agreeableness. A one standard deviation increase in agreeableness increases the predicted probability of cooperation by a subject with modal demographic characteristics from 67.9% to 80.6%.     

Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma

Cooperation in the finitely repeated prisoner's dilemma is justified, without departure from strict utility maximization or complete information, but under the assumption that there are bounds (possibly very large) to the complexity of the strategies that the players may use.     

央行的"囚徒困境"——评高额外汇储备对货币政策影响

近年来我国外汇储备高速增长以及2006年2月跃居世界第一成了国内外的焦点。高额外汇储备隐含的巨大风险及潜在成本已经引起了广泛关注。本文从高额外汇储备所蕴含的风险之一——高额外汇储备削弱央行货币政策独立性的角度,分三部分分析了当前我国外汇储备的问题。首先描述了当前我国外汇储备高速增长现象及原因,其次分析了高额外汇储备以及央行货币政策之间相互作用的机理及其潜在的风险,最后针对其潜在风险提出相应解决之道。     

Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring

We analyze repeated prisoners' dilemma games with imperfect private monitoring and construct mixed trigger strategy equilibria. Such strategies have a simple representation, where a player's action only depends upon her belief that her opponent(s) are continuing to cooperate. When monitoring is almost perfect, the symmetric efficient outcome can be approximated in any prisoners' dilemma game, while every individually rational feasible payoff can be approximated in a class of such games. The efficiency result extends when there are more than two players. It requires that monitoring be sufficiently accurate but does not require very low discounting when a public randomization device is available. Journal of Economic Literature Classification Numbers: C73, D82.     

海绵城市建设中政府、企业与公众的囚徒困境博弈分析

随着经济的发展,城镇化进程的加快,我国城市面临的生态环境问题日趋严峻,推进海绵城市建设已成为优化城市生态环境,治理水污染的有效途径。然而在海绵城市的建设过程中,政府、企业和公众作为参与主体,存在个体利益与集体利益、长期利益与短期利益的矛盾和冲突。基于上述问题,借助囚徒困境理论,分析海绵城市建设过程中政府、企业和公众三者的策略选择。研究表明,政府应当兼顾长远利益,扫除海绵城市建设中存在的障碍,加大海绵城市投资力度,企业和公众也应当积极主动参与到海绵城市的建设中来,从而实现三者利益最大化,以期能够为海绵城市的建设决策提供理论支撑。     

Beliefs and rationalizability in games with complementarities

We propose two characteristics of beliefs and study their role in shaping the set of rationalizable strategy profiles in games with incomplete information. The first characteristic, type-sensitivity, is related to how informative a player thinks his type is. The second characteristic, optimism, is related to how “favorable” a player expects the outcome of the game to be. The paper has two main results: the first result provides an upper bound on the size of the set of rationalizable strategy profiles; the second gives a lower bound on the change of location of this set. These bounds are explicit expressions that involve type-sensitivity, optimism, and payoff characteristics. Our results generalize and clarify the well-known uniqueness result of global games (Carlsson and van Damme, 1993). They also imply new uniqueness results and allow us to study rationalizability in new environments. We provide applications to supermodular mechanism design (Mathevet, 2010b) and information processing errors.     

Finite automata play the repeated prisoner's dilemma

The paper studies two-person supergames. Each player is restricted to carry out his strategies by finite automata. A player's aim is to maximize his average payoff and subject to that, to minimize the number of states of his machine. A solution is defined as a pair of machines in which the choice of machine is optimal for each player at every stage of the game. Several properties of the solution are studied and are applied to the repeated prisoner's dilemma. In particular it is shown that cooperation cannot be the outcome of a solution of the infinitely repeated prisoner's dilemma.     

On the Use of the Prisoners' Dilemma to Analyze the Relations Between Employment Security,Trust, And Effort

Sociologists and political scientists have argued that the explanatory adequacy of economics is undermined by unreasonable assumptions of rationality. Yet interpretations that make strong rationality assumptions remain common. Analyses of the effects of employment security on work effort provide one example. The iterated prisoners' dilemma has been used to deduce a positive effect of employment security on work effort. Several difficulties with this approach are identified, including that the cooperative solution to the iterated prisoners' dilemma game i) requires infinite play or uncertainty about the end of the repetitions of the game; ii) is made less likely where there are structural bases for divergent interests; iii) ignores the possibility that employers might choose to shift the game to another arena. In general, there is the difficulty that employer-employee relations involve three simultaneous prisoners' dilemmas. The paper concludes that the hyper-rational approach implied in the prisoners' dilemma is an unpromising route for the analysis of the effects of employment security.     

Transparency and cooperation in repeated dilemma games: a meta study

We use data from experiments on finitely repeated dilemma games with fixed matching to investigate the effect of different types of information on cooperation. The data come from 71 studies using the voluntary contributions paradigm, covering 122 data points, and from 18 studies on decision-making in oligopoly, covering another 50 data points. We find similar effects in the two sets of experimental games. We find that transparency about what everyone in a group earns reduces contributions to the public good, as well as the degree of collusion in oligopoly markets. In contrast, transparency about choices tends to lead to an increase in contributions and collusion, although the size of this effect varies somewhat between the two settings. Our results are potentially useful for policy making, because they provide guidance on the type of information to target in order to stimulate or limit cooperation.     

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.     

Hope springs eternal: learning and the stability of cooperation in short horizon repeated games

This paper considers learning rates in finitely repeated prisoners’ dilemmas. If players think their opponents might be relatively cooperative (e.g., tit-for-tat or grim types), they will cooperate in finitely repeated prisoners’ dilemmas (see Kreps et al., J. Econom. Theory 27 (1982) 245). However, if there are actually no cooperative types, players will eventually learn this and cooperation will break down. This paper shows that this learning is extremely slow, so it will take an extremely long time for cooperation to break down.Thus, suppose the world is either “good” or “bad.” The probability of a grim type is δ>0 if the world is good, and zero if the world is bad. Successive generations pair up to play finitely repeated prisoners’ dilemmas. Players observe play in previous generations and use Bayes’ rule to update their prior, π, that the world is good. We show that, if the world is really bad, then π falls per generation on average. Thus, if δ is small, there is less cooperation if the world is good, but cooperation may become more stable. For a representative 19 period repeated prisoners’ dilemma, beliefs fall one percentage point on average after a thousand generations.To derive these learning rates, we must refine existing results on the sensitivity of repeated games to Kreps et al. (1982) type perturbations. Specifically, we show cooperation is possible in perturbed prisoners’ dilemmas repeated O(log(1/δ)) times. This improves significantly on the O(1/δ) results in previous work. The paper thus provides two new reasons why cooperation tends to be stable, even in short horizon repeated games.     

The collective action problem: Within-group cooperation and between-group competition in a repeated rent-seeking game

This paper analyzes the ability of group members to cooperate in rent-seeking activities in a context of between-group competition. For this purpose, we develop an infinitely repeated rent-seeking game between two groups of different size. We first investigate Nash reversion strategies to support cooperative behavior in both groups, before analyzing double-edge trigger strategies which support cooperation in one group only. These last strategies have the property that cheating on the agreement in the cooperative group is followed by non-cooperation in this group and cooperation in the rival group. The main conclusion is that the set of parameters for which cooperation can be sustained within the larger group as a subgame perfect outcome is as large as that for which cooperation can be sustained in the smaller group. Hence, in contrast to Olson?s (1965) celebrated thesis, but in accordance with many informal and formal observations, larger groups can be as effective as smaller groups in furthering their interests.     

Choice, preference and rationalizability in pareto’s theory of economic behavior

Pareto initiated the shift of economic theory from utility/preference to choice in order to fill a gap between theoretical and empirical economics. His suggestions for an empirically-oriented theory of choice were to be developed decades later in the literature on revealed preference and on the conditions of equivalence between preference-based and choice-based axiomatic structures. In the process, however, substantial departures from Pareto’s implicit design of the situation of choice were introduced. In this paper, the conditions for the rationalizability of choice are re-defined so that they fit the type of situation that Pareto had in mind. The result is that the main consistency axioms of standard choice theory have to give way to a different combination of axioms that concern decisiveness as well as consistency. (JEL:B13, D01, D11).     

Endogenous leadership and sustainability of enhanced cooperation in a repeated interactions model of tax competition: Endogenous leadership in tax competition

In this study, the endogenous timing of moves is analyzed in an infinitely repeated game setting of capital tax competition between a subgroup (a tax union) of countries agreeing on partial tax harmonization and outside countries. It is shown that in a subgame perfect equilibrium of the infinitely repeated tax competition game, they simultaneously set capital taxes in every stage game when a tax union comprises similar countries with respect to productivity, whereas they may set capital taxes sequentially in every stage game when a tax union comprises dissimilar countries. This finding is significantly different from Ogawa (2013), although we also assume that capital is owned by the country's residents, as in Ogawa's model. This is because a disadvantaged member country of the tax union would suffer from larger losses when a tax union comprising dissimilar countries, and thus the tax union will choose the strategy of moving Late for the sake of sustaining tax harmonization to avoid such losses.     

西方知识分子的困境和理论

西方在近代社会通过知识分子这个阶层强烈地发展了一种“批判的建设性”,即对社会的贡献通过批判的建设来体现。这样的传统。与中国传统的知识分子的特征有很大不同。在中国,圣王真正参与朝政之中,可以选择与朝廷合作;如果不能合作,他仍可以在民间跟君道配合。实现士大夫的政治理想;如果朝政的道义基础彻底崩溃。他们也可以成为抗议精神的领袖,参与政治的空间是非常宽广的。     

社会统筹养老金供给的两难困境与政策选择

在中国养老保险制度建立与完善过程中,其主要矛盾仍然是如何筹资和如何给付的问题。社会统筹主要通过提高缴费率和扩大覆盖面两条途径来增加基金供给,而现行制度却面临着养老金供给的两难困境。一是提高缴费率增加了基金收入,但不利于经济增长与扩大覆盖面;二是不同群体实行差别费率有利于扩大覆盖面,但加剧了养老金收支的失衡。经数理模型与实证分析,社会统筹缴费率应该保持适度水平,同时应该对不同群体实行差别费率的政策进行调整,以建立养老保障的长效机制。