Perfect Bayesian Equilibria in Repeated Sales with Multiple Buyers

Abstract

In an auction with repeated sales of the same item, sellers try to learn buyers' values of the item and buyers try to hide it. At a Perfect Bayesian Equilibrium, sellers maximize their profit against buyers' strategies and buyers maximize their utilities against sellers' strategies. This thesis first explores the Perfect Bayesian Equilibrium structures in different auction settings that were studied in existing publications. Then, we add our original work to extend the current understanding of Perfect Bayesian Equilibrium ofrepeated sales to the multi-buyer settings where buyers' values for items are drawn from different distributions. We prove that under certain conditions, there is a Perfect Bayesian Equilibrium between a seller and two buyers with arbitrary distributions.