Second Price Auctions with Valuations and Participation Costs Both Privately Informed

This paper studies equilibria of second price auctions when valuations and participation costs are both private information with general distribution functions. We consider the existence and uniqueness of equilibrium in this general framework of two-dimensional types. It is shown that there always exists an equilibrium, and further there exists a unique symmetric equilibrium when all bidders are ex ante homogeneous. Moreover, we identify a sufficient condition under which there is a unique equilibrium in a heterogeneous economy with two bidders. Our general result includes many existing results as special cases.