Information Spillover in a Bayesian Repeated Game

Abstract

This paper considers an infinitely repeated three-player Bayesian game with lack of information on two sides, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a generalization of Aumann, Maschler and Stearns (1995) two-player zero-sum one-sided incomplete information model. Under a correlated prior, the informed player faces the problem of how to optimally disclose information among two uninformed players in order to maximize his long term average payoffs. The objective is to understand the adverse effects of “information spillover” from one game to the other in the equilibrium payoff set of the informed player. We provide conditions under which the informed player can fully overcome such adverse effects, and show that in some cases the adverse effects are unsurmountable and severe.