Equilibrium selection in interdependent value auctions

Abstract

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 notion of distributional strictly perfect equilibrium (DSPE) for Bayesian games with infinite type and action spaces. This equilibrium is robust against arbitrary small perturbations of strategies. We apply DSPE to a class of symmetric second-price auctions with interdependent values and show that the efficient equilibrium defined by Milgrom [27] is a DSPE, while a class of less intuitive, inefficient, equilibria introduced by Birulin [12] is not.