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.     

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.     

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.     

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.     

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.     

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.     

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.     

关于阿罗不可能定理的一个猜想

本文讨论了“阿罗不可能定理”的逻辑问题。同时指出,如果将效用函数放在非欧空间里考察,则“投票悖论”可以解决。本文还给出了效用函数在空间里的一个几何表示。     

A General Solution to King Solomon's Dilemma

In general terms, Solomon's dilemma is this. There are many agents. An object must be awarded at no cost to the one agent who values it most. We provide a mechanism that implements this outcome in iteratively weakly undominated strategies when it is common knowledge that the agent who most values the object knows who he is.Journal of Economic LiteratureClassification Numbers: C60, C72, D61, D74, D82.     

A Partial Rehabilitation of Hotelling's MC-Pricing Theorem

Harold Hotelling's celebrated theorem on the optimality of marginal cost pricing was criticized first by Frisch and later by Silberberg on the grounds that he did not use the marginal cost pricing condition in his original proof and hence that it did not constitute a valid proof. This note demonstrates that a key equation in Hotelling's proof is locally satisfied if and only if prices are set equal to marginal cost at the initial equilibrium and reexamines the validity of Hotelling's proof.     

A Characterization of Robust Sunspot Equilibria

In nonconvex environments, a sunspot equilibrium can sometimes be destroyed by the introduction of new extrinsic information. We provide a simple test for determining whether or not a particular equilibrium survives, or is robust to, all possible refinements of the state space. We use this test to provide a characterization of the set of robust sunspot-equilibrium allocations of a given economy; it is equivalent to the set of equilibrium allocations of the associated lottery economy. Journal of Economic Literature Classification Numbers: D51, D84, E32.     

浅探桂林民俗文化旅游

民俗文化旅游是一种高层次的文化旅游,它适应了现代旅游多元化发展的格局。广西桂林是一个多民族聚居地,是民俗文化旅游资源极其丰富的地区,民俗文化在桂林旅游业发展中起到了重要作用。因此有必要就桂林民俗文化旅游开发现状及发展中存在的问题进行阐述,并对其实现可持续发展提出相应的对策,以期为桂林的民俗文化旅游发展提供有益的参考价值。     

A Proof of Calibration via Blackwell's Approachability Theorem

Over the past few years many proofs of the existence of calibration have been discovered. Each of the following provides a different algorithm and proof of convergence: D. Foster and R. Vohra (1991, Technical Report, University of Chicago), (1998, Biometrika85, 379–390), S. Hart (1995, personal communication), D. Fudenberg and D. Levine (1999, Games Econ. Behavior29, 104–130), and S. Hart and A. Mas-Colell (1997, Technical Report, Hebrew University). Does the literature really need one more? Probably not. But the algorithm proposed here has two virtues. First, it only randomizes between two forecasts that are very close to each other (either p or p + ε). In other words, the randomization only hides the last digit of the forecast. Second, it follows directly from Blackwell's approachability theorem, which shortens the proof substantially. Journal of Economic Literature Classification Numbers: C70, C73, C53.