In defining random belief equilibrium (RBE) in finite, normal form games we assume a player's beliefs about others' strategy choices are randomly drawn from a belief distribution that is dispersed around a central strategy profile, the focus. At an RBE: (1) Each chooses a best response relative to her beliefs. (2) Each player's expected choice coincides with the focus of the other players' belief distributions. RBE provides a statistical framework for estimation which we apply to data from three experimental games. We also characterize the limit-RBE as players' beliefs converge to certainty. When atoms in the belief distributions vanish in the limit, not all limit-RBE (called robust equilibria) are trembling hand perfect Nash equilibria and not all perfect equilibria are robust.

We model a spatial market in which the utility of each consumer is affected by the consumers who buy precisely the same product. The marginal contribution of consumers x’s purchase on consumer y depends on | x - y |, which declines as | x - y| increases. Such modelling of preferences fits goods that signal a consumer’s place in society—clothing styles, automobiles and jewellry are examples. For 2 n + 1 firms we find the unique symmetric equilibrium and derive comparative statics on the optimal number of firms, the largest number of firms the market can support, and the behaviour of profits per firm as n increases.

Abstract We examine a club model in which the club's policies are controlled by a homogeneous group of insiders. Their policy decision is to determine the number they will admit from two outsider groups. Countries have immigration policies, private clubs have membership policies, and professional practices also have membership criteria in which individuals may be screened. In all these organizations new members bring a material benefit to the organization, but do so at the cost of introducing a socially differentiated population of outsiders that the majority typically dislikes. It is the interplay of the material benefit and the social cost on which we focus. We characterize steady state equilibria and examine comparative statics results.

We propose a dynamic model of n-firm oligopoly that provides a logically consistent reinterpretation of conjectural variations. Each firm solves a dynamic optimization problem believing that the other firms will alter their future choices in proportion to its own current change. These beliefs adapt in light of observed behavior. We show that steady state equilibria can range from complete cooperation to predatory play and provide conditions under which the firms’ behavior and beliefs converge to a steady state. The sufficient conditions for stability are more easily satisfied the smaller the cross-effects among firms through demand or belief parameters. They are also more easily satisfied in a price setting than in a quantity setting, differentiated products model.

We study repeated interactions among a fixed set of “low rationality” players who have status quo actions, randomly sample other actions, and change their status quo if the sampled action yields a higher payoff. This behavior generates a random process, the better-reply dynamics. Long run behavior leads to Nash equilibrium in games with the weak finite improvement property, including finite, supermodular games and generic, continuous, two-player, quasi-concave games. If players make mistakes and if several players can sample at the same time, the resulting better-reply dynamics with simultaneous sampling converges to the Pareto optimal Nash equilibrium in common interest games. Journal of Economic Literature Classification Numbers: C70, C72, C73.

Entendu dans un sens un large, l'héritage de Cournot pour les économistes consiste (i) en ce qu'il a montré comment utiliser de manire générale les mathématiques pour développer des théories économiques, au lieu d'avoir recours des exemples reposant sur des formes fonctionnelles spécifiques, (ii) en ce qu'il a donné un traitement clairet sophistiqué de la demande de marché, du monopole, des marchés concurrentiels et, avant tout, de l'oligopole. Les économistes contemporains se souviennent seulement de Cournot pour sa théorie de l'oligopole. Cependant, il semble avoir eu une grande influence sur Marshall et Walras, ainsi que sur d'autres économistes moins enclins aux mathématiques.

We develop a model with heterogeneous buyers and sellers in which the sellers have private information about their goods' qualities. We show that efficient trading cannot occur without middlemen. Middlemen can provide two services: one is inspection, and the other is the sorting of buyers and sellers through the rationing of sellers and the provision of two different price schedules. The latter service permits the possibility of achieving the first best. When the first best is not attainable, there is a second best characterized by two intervals, one consisting of low‐quality noninspected goods, and the other of high‐quality inspected goods. We determine whether first and second best outcomes can be implemented in a market equilibrium with both zero and infinite buyer‐seller search costs. First and second best outcomes are attainable under a larger set of parameter values when search costs are infinite; also, typically too much inspection occurs in a market equilibrium. Welfare may be either raised or lowered by the introduction of middlemen.

This paper analyzes games with imperfectly enforceable agreements. It develops a dynamical model in which players are randomly paired into single shot games at each moment. Initially players decide whether to honor an agreement, and then they choose whether to complain to an enforcement agency. The probability of success of a complaint is endogenous; it depends upon whether the defendant breached and upon the aggregate behavior of all players. In the most interesting equilibria of the dynamical system some individuals honor and some individuals complain while others do not, and the net effect of the existence of an enforcement agency is positive.Journal of Economic LiteratureClassification Number: C72.

We propose an equilibrium forn-person finite games based on bounded rationality using the logit model of discrete choice theory. At equilibrium, each player uses appropriate choice probabilities, given those used by the others. Rationality is parameterized on a continuum from complete rationality to uniform random choice. Results on the existence of equilibrium and on convergence to Nash as rationality becomes perfect are similar to results due to McKelvey and Palfrey. We identify conditions such that for a given rationality parameter range the path of choices over time when the players use fictitious play converges to equilibrium.Journal of Economic LiteratureClassification Numbers: C72, L20.

This paper investigates the impact of antitrust policy on the strategic choice of product specification when firms can collude with respect to prices, cannot collude with respect to location and may have their collusion ended if it is detected by the antitrust authority. Depending on the aggressiveness of the antitrust authority, different location configurations may emerge in equilibrium. Extremely aggressive and extremely lax policies lead to the least efficient outcomes while the configuration maximizing social welfare is obtained by an intermediate policy.

We analyze an experience good model with producer moral hazard which is based on Shapiro (Quarterly Journal of Economics, 1983, 98, 659–679). We develop conditions under which a good will be sold through a middleman instead of being sold directly by the producer when selling costs may even be increased by the presence of middlemen. Middlemen help to alleviate the producer moral hazard problem by dropping a producer's good, and lowering her future sales, if the good is not of its claimed quality. The middleman engages in this policing activity in order to maintain his own reputation as a seller of high quality goods.

Friedman and Samuelson (1990, Games Econ. Behav. 2, 304–324) have recently shown that continuous reaction functions can support nontrivial outcomes as subgame perfect equilibria in repeated games. This paper examines continuous reaction functions in duopolies. We first establish a folk theorem, showing that any feasible, individually rational outcome in the stage game can be supported as a subgame perfect equilibrium outcome in continuous reaction functions (given sufficiently high discount factors). We then show that the set of discount factors for which outcomes can be supported by continuous reaction functions is at least as large as the corresponding sets under Nash reversion trigger strategies and optimal two-phase symmetric punishments. The implication of these findings is that no generality in terms of possible equilibrium outcomes need be sacrificed in the course of requiring continuity. Journal of Economic Literature Classification Numbers: D43, C72.