Articles

Learning the state of nature in repeated game with incomplete information and signals

J. Renault, T. TOMALA

Games and Economic Behavior

avril 2004, vol. 47, n°1, pp.124-156

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


Author Keywords: incomplete information; repeated games; imperfect monitoring; completely revealing equilibria; communication; Byzantine agreement Keywords Plus: COMMUNICATION Abstract: The motivation of this paper comes from repeated games with incomplete information and imperfect monitoring. It concerns the existence, for any payoff function, of a particular equilibrium (called completely revealing) allowing each player to learn the state of nature. We consider thus an interaction in which players, facing some incomplete information about the state of nature, exchange messages while imperfectly monitoring them. We then ask the question: can players learn the true state even under unilateral deviations? This problem is indeed closely related to Byzantine agreement problems from computer science. We define two different notions describing what a player can learn if at most one other player is faulty. We first link these notions with existence of completely revealing equilibria, then we characterize them for monitoring structures given by a graph. As a corollary we obtain existence of equilibria for a class of undiscounted. repeated games


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