中文摘要
我们考虑如下设定:标准式博弈的每一位参与人在博弈开始前各自私下设计一个信息结构,其中一个设计被随机选中,用以确定参与人所收到的私人消息的分布。这些消息使参与人能够使其行动相互关联;然而,私人信息设计意味着一种从相关均衡向纳什均衡的推动。事实上,该私人信息设计扩展式博弈的序贯均衡支付就是底层标准式博弈的相关均衡支付,但并非所有相关均衡支付都是序贯均衡支付。在通有的两人博弈中,后者是两个纳什均衡支付的特定凸组合。在任意两人博弈中,通过施加由私人信息设计得到的最优信念,我们可以获得纳什均衡的充分认知条件,而这些条件仅要求关于参与人理性的知识。
Abstract
We consider a setting where each player of a normal-form game privately designs an information structure before playing the game. One of these designs is chosen at random to determine the distribution of the private messages that players receive. These messages allow players to correlate their actions; however, private information design implies a push from correlated to Nash equilibria. Indeed, the sequential equilibrium payoffs of the private information design extensive-form game are correlated equilibrium payoffs of the underlying normal-form game, but not all correlated equilibrium payoffs are sequential equilibrium payoffs. In generic 2-player games, the latter are specific convex combinations of two Nash equilibrium payoffs. In any 2-player game, imposing optimal beliefs from private information design allows us to obtain sufficient epistemic conditions for Nash equilibrium that require only knowledge of players' rationality.