Beliefs and Public Good Provision with Anonymous Contributors

We analyze a static game of public good contributions where finitely many anonymous players have heterogeneous preferences about the public good and heterogeneous beliefs about the distribution of preferences. In the unique symmetric equilibrium, the only individuals who make positive contributions are those who most value the public good and who are also the most pessimistic; that is, according to their beliefs, the proportion of players who most like the public good is smaller than it would be according to any other possible belief. We predict whether the aggregate contribution is larger or smaller than it would be in an analogous game with complete information and heterogeneous preferences, by comparing the beliefs of contributors with the true distribution of preferences. A trade‐off between preferences and beliefs arises if there is no individual who simultaneously has the highest preference type and the most pessimistic belief. In this case, there is a symmetric equilibrium, and multiple symmetric equilibria occur only if there are more than two preference types.     

Farsightedness in a Coalitional Great Fish War

We explore the implications of the farsightedness assumption on the conjectures of players in a coalitional Great Fish War model with symmetric players, derived from the seminal model of Levhari and Mirman (Bell J Econ 11:649–661, 1980). The farsightedness assumption for players in a coalitional game acknowledges the fact that a deviation from a single player will lead to the formation of a new coalition structure as the result of possibly successive moves of her rivals in order to improve their payoffs. It departs from mainstream game theory in that it relies on the so-called rational conjectures, as opposed to the traditional Nash conjectures formed by players on the behavior of their rivals. For values of the biological parameter and the discount factor more plausible than the ones used in the current literature, the farsightedness assumption predicts a wide scope for cooperation in non-trivial coalitions, sustained by credible threats of successive deviations that defeat the shortsighted payoff of any prospective deviator. Compliance or deterrence of deviations may also be addressed by acknowledging that information on the fish stock or on the catch policies actually implemented may be available only with a delay (dynamic farsightedness). In that case, the requirements are stronger and the sizes and number of possible farsighted stable coalitions are different. In the sequential move version, which could mimic some characteristics of fishery models, the results are not less appealing, even if the dominant player or dominant coalition with first move advantage assumption provides a case for cooperation with the traditional Nash conjectures.     

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

In this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.     

Learning to alternate

The Individual Evolutionary Learning (IEL) model explains human subjects’ behavior in a wide range of repeated games which have unique Nash equilibria. Using a variation of ‘better response’ strategies, IEL agents quickly learn to play Nash equilibrium strategies and their dynamic behavior is like that of humans subjects. In this paper we study whether IEL can also explain behavior in games with gains from coordination. We focus on the simplest such game: the 2 person repeated Battle of Sexes game. In laboratory experiments, two patterns of behavior often emerge: players either converge rapidly to one of the stage game Nash equilibria and stay there or learn to coordinate their actions and alternate between the two Nash equilibria every other round. We show that IEL explains this behavior if the human subjects are truly in the dark and do not know or believe they know their opponent’s payoffs. To explain the behavior when agents are not in the dark, we need to modify the basic IEL model and allow some agents to begin with a good idea about how to play. We show that if the proportion of inspired agents with good ideas is chosen judiciously, the behavior of IEL agents looks remarkably similar to that of human subjects in laboratory experiments.     

AN EXPERIMENT WITH ULTIMATUM BARGAINING IN A CHANGING ENVIRONMENT*

We present experimental results on the ultimatum bargaining game which support an evolutionary explanation of subjects’ behaviour in the game. In these experiments subjects interacted with each other and also with virtual players, i.e. computer programs with pre‐specified strategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behaviour closer to the subgame‐perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behaviour of real subjects depending on the type of “mutants” (virtual players) that were present in their environment.     

Evolutionary selection of ‘chivalrous’ conventions in coordination games without common expectations

We study an evolutionary game-theoretic model where players have to choose within a predetermined set of mixed strategies in a coordination game. Players are of two different kinds, male and female. No common expectations assumption is made; players tend therefore to adopt the strategy that yields larger than average expected payoffs for their kind. In this framework, every stable stationary point of the population dynamics can be interpreted as the emergence of a particular convention. A classification of the possible conventions is provided; conditions for their emergence are determined.     

Relative versus Absolute Speed of Adjustment in Strategic Environments: Responder Behavior in Ultimatum Games

Learning models predict that the relative speed at which players in a game adjust their behavior has a critical influence on long term behavior. In an ultimatum game, the prediction is that proposers learn not to make small offers faster than responders learn not to reject them. We experimentally test whether relative speed of learning has the predicted effect, by manipulating the amount of experience accumulated by proposers and responders. The experiment allows the predicted learning by responders to be observed, for the first time.     

送转与定向增发：基于市值管理的视角

送转和定向增发是 A 股市场上常见的两种公司行为。文章旨在从市值管理的视角，揭示上市企业送转与定向增发的内在关联及其经济逻辑。研究发现：(1)定向增发企业送转的比例与规模显著高于配对的未增发企业，而且两者的差异在增发后显著大于增发前；(2)在有外部机构投资者参与的定向增发中，企业送转的比例与规模显著高于其他类型的定向增发；(3)企业送转行为会显著影响增发折价，增发后送转企业的增发折价显著低于增发前送转(从未送转)的企业。文章研究表明，送转是 A 股市场上定向增发企业广为使用的一种市值管理手段，送转的规模与时机是企业与外部投资者理性博弈的结果。文章的研究不仅从市值管理角度为我国资本市场上频频出现的上市公司高送转行为提供了经验证据，而且对于监管层制定与送转和定向增发相关的政策具有重要的参考价值。     

Behavior and Learning in the “Dirty Faces” Game

This paper examines the Dirty Faces problem as a Bayesian game. The equilibrium in the general form of the game requires the extreme assumption of common knowledge of rationality. However, for any finite number of players, the exact number of steps of iterated rationality necessary for the equilibrium to arise depends on the number of players of a particular type, allowing the game to be used to bound the number of steps satisfied by actual players. The game differs from other games used to study iterated rationality in that all players are better off when common knowledge of rationality is satisfied. While behavior in experiments is inconsistent with the game-theoretic prediction at the group level, individual level behavior shows a greater degree of consistency with theory and with previous results on iterated rationality. Finally, there is some evidence of learning in repeated play.     

Drugs,guns, and targeted competition

We consider a dynamic competition game involving three players, in which each player can vary the extent of his competition on a per-rival basis. We call such competition targeted. We show that if the players are myopic, then the weaker players eventually lose the game to their strongest rival. If instead the players are sufficiently far-sighted, then all three players converge in their power and stay in the game. We develop our model in application to drug wars, but the approach of targeted competition can be applied to competition between firms or political parties, or to warfare.     

Essential equilibria of large generalized games

We characterize the essential stability of games with a continuum of players, where strategy profiles may affect objective functions and admissible strategies. Taking into account the perturbations defined by a continuous mapping from a complete metric space of parameters to the space of continuous games, we prove that essential stability is a generic property and every game has a stable subset of equilibria. These results are extended to discontinuous large generalized games assuming that only payoff functions are subject to perturbations. We apply our results in an electoral game with a continuum of Cournot-Nash equilibria, where the unique essential equilibrium is that only politically engaged players participate in the electoral process. In addition, employing our results for discontinuous games, we determine the stability properties of competitive prices in large economies.     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

基于博弈论的企业激励制度分析——从经济学视角看“不能让老实人吃亏”

将制度定义为博弈的规则,应用现代博弈论的方法论证了企业为什么不能让老实人吃亏,并探讨了企业有效激励制度的设计思路。本文引入新制度经济学人的有限理性假设,建立一个有限博弈方的进化博弈模型,证明了如果不能从制度上保证不让老实人吃亏,具有机会主义行为倾向的员工在重复博弈之后最终都将选择偷懒。并分两种情况分析了企业如何设计有效的激励制度,从而从制度上保证不让老实人吃亏。     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

A strategic analysis of global warming: Theory and some numbers

We model the global warming process as a dynamic commons game in which the players are countries, their actions at each date produce emissions of greenhouse gases, and the state variable is the current stock of greenhouse gases. The theoretical analysis is complemented by a calibration exercise. The first set of results establishes theoretically, and then with illustrative numbers, the over-emissions due to a “tragedy of the commons.” The power of simple sanctions to lower emissions and increase welfare is then examined as is the effect of cost asymmetry. Finally, a complete theoretical charactrization is provided for the best equilibrium, and it is shown that it has a very simple structure; it involves a constant emission rate through time.     

Cooperation,imitation and partial rematching

We study a setting in which imitative players are matched into pairs to play a Prisonerʼs Dilemma game. A well-known result in such setting is that under random matching cooperation vanishes for any interior initial condition. The novelty of this paper is that we consider partial rematching: players that belong to a pair in which both parties cooperate repeat partner next period, while all other players are randomly matched into pairs. Under certain conditions, this rematching mechanism makes cooperation the unique outcome in the long run. Furthermore, we show that if imitation happens infrequently enough then cooperative behavior is always present in the population.     

Extinction in common property resource models: an analytically tractable example

We discuss an analytically tractable discrete-time dynamic game in which a finite number of players extract a renewable resource. We characterize a symmetric Markov-perfect Nash equilibrium of this game and derive a necessary and sufficient condition under which the resource does not become extinct in equilibrium. This condition requires that the intrinsic growth rate of the resource exceeds a certain threshold value that depends on the number of players and on their time-preference rates.     

Mindreading and endogenous beliefs in games

We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs.     

Partial exposure in large games

In this work we introduce the notion of partial exposure, in which the players of a simultaneous-move Bayesian game are exposed to the realized types and chosen actions of a subset of the other players. We show that in any large simultaneous-move game, each player has very little regret even after being partially exposed to other players. If players are given the opportunity to be exposed to others at the expense of a small decrease in utility, players will decline this opportunity, and the original Nash equilibria of the game will survive.     

Bargaining foundation for ratio equilibrium in public‐good economies

We provide a bargaining foundation for the concept of ratio equilibrium in public‐good economies. We define a bargaining game of alternating offers, in which players bargain to determine their cost shares of public‐good production and a level of public good. We study the stationary subgame perfect equilibrium (SSPE) without delay of the bargaining game. We demonstrate that when the players are perfectly patient, they are indifferent between the equilibrium offers of all players. We also show that every SSPE without delay in which the ratios offered by all players are the same leads to a ratio equilibrium. In addition, we demonstrate that all equilibrium ratios are offered by the players at some SSPE without delay. We use these results to discuss the case when the assumption of perfectly patient players is relaxed and the cost of delay vanishes.