Optimal Commitments in Single-Item Auctions

Understanding Bayesian Nash equilibria (BNE) in auctions with asymmetric bidders has been an important research agenda in auction theory. However, to date, little has been known about this problem in general cases. In this talk, we consider an alternative solution concept, called Bayes commitment (Bayes Stackelberg equilibrium) that only requires best response on one side. We fully characterize optimal commitment in a class of single-item auctions, including first price auction and all-pay auctions. Based on the characterization, we further obtain closed-form solutions of optimal commitments under general conditions of valuation distributions. The solutions reveal interesting phenomenons such as collusion, threat and overbidding.