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
