Second-price Auction with Two-Dimensional Private Information on Values and Participation Costs

This paper studies equilibria of second price auctions when values and participation costs are both privation information and are drawn from general distribution functions. We consider the existence and uniqueness of equilibrium. It is shown that there always exists an equilibrium for this general economy, and further there exists a unique symmetric equilibrium when all bidders are ex ante homogenous. Moreover, we identify a sufficient condition under which we have a unique equilibrium in a heterogenous economy with two bidders. Our general framework covers many relevant models in the literature as special cases.