Sequential Equilibria in Bayesian Games with Communication

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games.Bayesian games, Communication, Communication equilibrium, Sequential communication equilibrium

Sequential Equilibria in Bayesian Games with Communication

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games

Communication in Bayesian games: Overview of work on implementing mediators in game theory.

game theory; Bayesian games;

Strategic Knowledge Sharing in Bayesian Games: Applications

This paper studies the properties of endogenous information structures in some classes of Bayesian games in which a first stage of strategic information revelation is added. Sufficient conditions for the existence of perfectly revealing or non-revealing equilibria are characterized. In particular, the existence of a perfectly revealing equilibrium is demonstrated for linear Bayesian games with an ordered information structure. Those games include, for example, Cournot games with incomplete information about the cost or the demand of industry, when firms may face any level of higher-order uncertainty. Several examples and different economic applications are examined to illustrate other results presented in the paper.Strategic information revelation; Bayesian games; Endogenous information structure; Certifiability.

Correlated equilibria and communication in games.

Analyse bayésienne; Théorie des jeux; Information privée;

Auctions with Severely Bounded Communication

We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g., that in optimal mechanisms bidders simply report the interval in which their valuation lies in, as well as some surprising properties, e.g., that asymmetric auctions are better than symmetric ones and that multi-round auctions reduce the communication complexity only by a linear factor

Bank Runs Without Sunspots

The literature on bank runs reduces all coordination mechanisms triggering attacks on banks to exogenous sunspots. We present a general equilibrium version of these models where the uncertainty faced by depositors is modeled explicitly, such that bank runs arise as optimal equilibrium outcomes corresponding to Bayesian coordination games played by rational agents before depositing. Differentials in information sets between the bank and its depositors lead to rational self-contained equilibrium runs. The coexistence of different beliefs in equilibrium jointly with the self-fulfilling nature of the attacks follow from Adam Smith's invisible hand principle. The runs obtained do not violate the revelation principle.La literatura sobre pánicos bancarios reduce todo mecanismo de coordinación que de lugar a los ataques a puntos solares exógenos. Presentamos una versión de equilibrio general de dichos modelos en la cual la incertidumbre a la que los agentes económicos se hallan sujetos es modelizada de forma explícita, de manera que los pánicos surgen como resultados óptimos de equilibrio correspondientes a juegos de coordinación Bayesianos jugados por agentes racionales antes de depositar sus fondos en el banco. Diferencias en los conjuntos de información entre el banco y sus clientes dan lugar a pánicos racionales autocontenidos en equilibrio. La coexistencia de diversas creencias probabilísticas en equilibrio, así como la naturaleza auto-contenida de los ataques, derivan del principio de la mano invisible de Adam Smith. Los pánicos obtenidos no violan el principio de revelación.Bank runs, Self-contained attacks, Bayesian coordination games, Revelation principle, Invisible hand principle, Pánicos bancarios, Ataques autocontenidos, Juegos de coordinación Bayesianos, Principio de revelación, Principios de la mano invisible.