When the demand functions depend on a one-dimensional private parameter, the two-unit pay-your-bid auction with two homogeneous bidders is equivalent to the one-unit first price auction with two heterogeneous bidders. The existence and uniqueness of the equilibrium of the pay-your-bid auction,...

The first price auction is the auction procedure awarding the item to the highest bidder at the price equal to his bid. Much attention has been devoted to the two bidder case or to the symmetric case where the bidders' valuations are identically and independently distributed. We consider the...