Distributional Perfect Equilibrium in Bayesian Games with Applications to Auctions

In second-price auctions with interdependent values, bidders do not necessarily have dominant strategies. Moreover, such auctions may have many equilibria. In order to rule out the less intuitive equilibria, we define the notions of distributional perfect and strong distributional perfect equilibria for Bayesian games with infinite type and action spaces. We prove that every Bayesian game has a distributional perfect equilibrium provided that the information structure of the game is absolutely continuous and the payoffs are continuous in actions for every type. We apply strong distributional perfection to a class of symmetric second-price auctions with interdependent values and show that the efficient equilibrium defined by Milgrom [22] is strongly distributionally perfect, while a class of less intuitive, inefficient, equilibria introduced by Birulin [11] is not.