Equilibria in Second Price Auctions with Private Participation Costs

We study equilibria in second price auctions when bidders are independently and privately informed about both their values and participation costs and their joint distributions across bidders are not necessarily identical. We show that there always exists an equilibrium in this general setting with two dimensional types of ex ante heterogeneous bidders. We provide conditions under which the equilibrium is unique. Moreover, when the bidders are ex ante symmetric, we show that there is a unique symmetric equilibrium. We also identify sufficient conditions for existence of asymmetric equilibria.