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.

翻译：本文审议了一个无限重复的三玩家贝叶西亚游戏,其中双方缺乏信息,知情玩家在每个阶段对两个不知情玩家同时玩两场零和游戏。这是对Aumann等人(Aumann et al.) [1] 的一般信息模式[1] 双玩家零和单向不完全信息模式。在一个相关之前,知情玩家面临如何在两个不知情玩家之间最佳披露信息以最大限度地实现他的长期平均回报的问题。我们的目标是理解在知情玩家的均衡报酬设置中,\信息从一个游戏向另一个游戏溢出的不利影响。我们提供了条件,让知情玩家能够完全克服这种不利影响并描述平衡报酬。在第二个结果中,我们展示信息溢出对知情玩家平衡报酬组合的影响如何严重。