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.     

Education Signalling with Preemptive Offers

We analyse a version of Spence's job market signalling model in which firms can make job offers before workers complete their education. Workers cannot commit to turning down such offers. Offers are private, so that workers are unable to use one firm's offer in an attempt to elicit better offers from other firms. In the unique sequential equilibrium outcome of the model with unproductive education, there is no wasteful education. When education is productive, the standard model predicts that more able individuals become overeducated to separate themselves from less able workers. In our model, less able workers become overeducated to (partially) pool with more able workers. The pooling mutes the incentives of high ability workers, who in consequence actually choose to become undereducated. We examine the robustness of our result to modifications to the basic model.     

High Price Strategy and Quality Signalling

I investigate a high price strategy by a durable‐goods producer for signalling the high quality of goods. It is assumed that two types of monopolists exist: high‐quality and low‐quality. The monopolist's type is assumed to be unknown to consumers in the first period. Before the beginning of the second period, a product reputation established in the past period enables consumers to recognize the real type of the monopolist. I show that there occurs a signalling equilibrium where the high‐quality type monopolist uses a high price strategy. An interaction between the new and old products peculiar to the durable‐goods markets plays an important role in the pricing strategy.     

Common Pool Games are Convex Games

For the class of cooperative common pool games the paper focuses on the question of how, during the preplay negotiation process, the ability of coalitions to enforce their claims imposes externalities on the opposition by having an impact on the jointly produced resource. One of our main results is that common pool games are clear games. Based on this result we are able to derive sufficient conditions for the convexity of the characteristic function, which establishes the second main result in the paper, namely that cooperative common pool games are characterized by increasing returns with respect to the coalition size.     

Calvin's Reformation in Geneva: Self and Social Signalling

As Weber ( 1904 ) recognized, Calvinistic beliefs about predestination may constitute a powerful incentive for good works; an individual wishes to receive assurances about her future prospects of salvation, and good works may provide a positive signal about such prospects. These beliefs can in turn create a social pressure to behave well, as good works can also signal to others that individuals belong to the “elect” and are therefore likely to behave well in social interactions. Moreover, the Consistory, an institution created by Calvin to monitor and publicize individuals' behavior, can allow for such social signalling. We analyze these self and social signalling incentives, and show how religions affect levels of cooperation and coordination.     

Reputation and Survival: Learning in a Dynamic Signalling Model

We consider the impact of reputation on the survival of a monopolist selling single units in discrete time periods, whose quality is learned slowly. If the seller learns her own quality at the same rate as customers, a sufficiently bad run of luck could induce her to stop selling. When she knows her quality, a good seller never stops selling though at low reputations a bad seller does with some probability. Furthermore, a seller with positive, though imperfect, information sells for the same number of periods whether her information is private or public. We further consider the robustness of the central result when the seller's opportunities for strategic behaviour are limited.     

Ambiguous Games

This paper introduces ambiguous games, a modification of the normal form that allows the presence of vagueness in players' beliefs over the opponents' choice of strategies. An appropriate notion of equilibrium is presented, and a general existence result is proved. Journal of Economic Literature Classification Numbers: C72, D81.     

Knowledge Games

The subject of epistemic logic is firmly entrenched in game theory, including the analysis of common knowledge and of public announcements, such as in 'hat problems'. How to analyse communications to sub groups of the public, and the effects of such common knowledge of a subgroup on the information state of a larger group, has only recently come into fruition. Knowledge games are introduced to provide a comfortably concrete vehicle for the study of such interactions. This paper introduces the concepts of knowledge game, deal of cards, knowledge game state, game action, and action execution. A deal of cards is a function from cards to players. A knowledge game state is represented by a pointed multiagent S5 model on the set of card deals where all players hold the same number of cards as in the actual deal. A game action combines a question with an answer, and is represented by a pointed multiagent S5 frame on the set of possible answers. The execution of a game action in a knowledge game state corresponds to the computation of a pointed multiagent S5 model that is a restriction of the direct product of the corresponding action frame and game model.     

Network Games

In contexts ranging from public goods provision to information collection, a player's well-being depends on his or her own action as well as on the actions taken by his or her neighbours. We provide a framework to analyse such strategic interactions when neighbourhood structure, modelled in terms of an underlying network of connections, affects payoffs. In our framework, individuals are partially informed about the structure of the social network. The introduction of incomplete information allows us to provide general results characterizing how the network structure, an individual's position within the network, the nature of games (strategic substitutes vs. complements and positive vs. negative externalities) and the level of information shape individual behaviour and payoffs.     

Action-Graph Games

Representing and reasoning with games becomes difficult once they involve large numbers of actions and players, because the space requirement for utility functions can grow unmanageably. Action-Graph Games (AGGs) are a fully-expressive game representation that can compactly express utility functions with structure such as context-specific independence, anonymity, and additivity. We show that AGGs can be used to compactly represent all games that are compact when represented as graphical games, symmetric games, anonymous games, congestion games, and polymatrix games, as well as games that require exponential space under all of these existing representations. We give a polynomial-time algorithm for computing a player's expected utility under an arbitrary mixed-strategy profile, and show how to use this algorithm to achieve exponential speedups of existing methods for computing sample Nash equilibria. We present results of experiments showing that using AGGs leads to a dramatic increase in the size of games accessible to computational analysis.²     

Strategic Trade Policy and Signalling with Unobservable Costs

In an environment in which home firm costs are private information, home firm output can signal these costs to a foreign competitor and a home policymaker. High-cost home firms have an incentive to misrepresent themselves as low-cost. This is understood by the foreign firm and the home policymaker and results in the first-period optimal per-unit output subsidy to the home firm being less than it would be if home firm output was not a signal of home firm costs. These results are extended to the case of simultaneous signalling and signalling through price.     

Altruism in Anonymous Dictator Games

We conduct double-anonymous dictator experiments to explore the role of altruism in motivating subjects' behavior. We vary the extent to which an anonymous recipient is deserving of aid and investigate its effect on the allocation of a fixed pie by student subjects. This is accomplished by including as treatments: (1) an anonymous student subject and (2) an established charity. We find that a significant increase in donations occurs when we increase the extent to which a donation goes to a recipient generally agreed to be “deserving.” We conclude that subjects are rational in the way they incorporate fairness into their decisions.Journal of Economic LiteratureClassification Numbers: A13, C91, D64.     

Market Games in Successive Oligopolies

This paper introduces a new approach to successive oligopolies. We draw on market games à la Shapley–Shubik to examine how successive oligopolies operate between downstream and upstream markets when the input price is determined by the action of all firms, downstream and upstream both. This approach differs from the classical one as it allows us to consider downstream firms that exercise market power both in both downstream and upstream markets. We perform a comparison of the market outcome with each scenarios as well as a welfare analysis.     

Strong Equilibrium in Congestion Games

[6]introduced the class of congestion games and proved that they always possess a Nash equilibrium in pure strategies. Here we obtain conditions for the existence of a strong equilibrium in this class of games, as well as for the equivalence of Nash and strong equilibria. We also give conditions for uniqueness and for Pareto optimality of the Nash equilibrium. Except for a natural monotonicity assumption on the utilities, the conditions are expressed only in terms of the underlying congestion game form. It turns out that avoiding a certain type of bad configuration in the strategy spaces is essential to positive results.Journal of Economic LiteratureClassification Numbers: C71, C72, D62.     

Correlated Equilibrium in Stochastic Games

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and is drawn according to the same probability distribution at every stage). We prove that any n-player stochastic game admits an autonomous correlated equilibrium payoff. When the game is positive and recursive, a stationary correlated equilibrium payoff exists. Journal of Economic Literature Classification Numbers: C72, C73.     

Self-Fulfilling Mechanisms in Bayesian Games

Amechanismfor a Bayesian gameGis a mapping μ from the set of states of nature to the set of players' actions. μ isself-fulfillingif players are truthful at the communication stage and, given the information revealed by μ, no player can gain in unilaterally deviating from the action prescribed by the mechanism. We investigate the properties of self-fulfilling mechanisms and we show in particular that they correspond to inert solutions of the infinitely repeated game generated byG. We also discuss applications to market games, regulation, and R&D games.Journal of Economic LiteratureClassification Numbers: D82, C72.     

博弈论的新发展:行为博弈论

标准博弈论在经济理性假设下分析博弈参与者如何在追求各自最优目标的同时实现均衡。但是,由于现实行为人是有限理性的,标准博弈论对实践的解释和指导受到限制。为了延伸博弈论对现实活动的解释,行为博弈论将实验经济学与标准博弈论相融合,在博弈实验的基础上,考察和解释标准理论推断与实验结果之间的差异,引入行为因素改进标准博弈论的基本假定,重构博弈分析模型,以求达到准确解读有限理性的行为人在现实约束中如何行动的目的。     

Extendable Cooperative Games

A (TU) cooperative game is extendable if every core allocation of each subgame can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its subgames can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core. Further, we characterize extendability in terms of an extension of the balanced cover of the game. It is also shown how this extension can unify the analysis of many families of games under one roof.