  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 the Aumann et al. [1] 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. Our 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 characterize equilibrium payoffs. In a second result, we show how
the effects of information spillover on the equilibrium payoff set of the
informed player might be severe.
