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Learning Sets in State Dependent Signalling Game Forms: A Characterization

CEREMADE, Université Paris IX Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
renault{at}ceremade.dauphine.fr

We consider repeated game forms with incomplete information and state dependent signalling structure. We study the information a player can learn about the state of nature through a communication procedure, in a way robust to unilateral deviations. More precisely, we say that player i can distinguish state from state ' if there exists a strategy profile such that if is the true state and at most one player deviates from the profile, then player i will know after a finite number of stages that ' is not the true state. The learning set of player i at is the set of states that player i cannot distinguish from . It corresponds to the information player i can learn, in a way immune against unilateral deviations, if the state is and players communicate through the game form for a finite number of stages. This notion was introduced in a joint paper with T. Tomala (Renault and Tomala 2000). We provide here a general characterization of the learning sets.

Key Words: Repeated games; signalling; learning set
History: Received: August 12, 1998; revision received: December 24, 2000;revision received: April 4, 2001;