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：本文考虑一种具有双方信息不完全性的无限重复三人贝叶斯博弈，其中知情博弈者在每一阶段同时与两位不知情博弈者进行两个零和博弈。这是Aumann等人[1]提出的两人零和单边不完全信息模型的推广。在相关先验条件下，知情博弈者面临如何最优地在两位不知情博弈者之间披露信息以最大化其长期平均收益的问题。我们的目标是理解从一博弈向另一博弈的"信息溢出"对知情博弈者均衡收益集的不利影响。我们提供了知情博弈者能够完全克服此类不利影响的条件，并刻画了均衡收益。在第二个结论中，我们展示了信息溢出对知情博弈者均衡收益集的影响可能十分严重。