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...

Despite the complexity of the first price auction in the general asymmetric case, analytical results have started to emerge in the literature. Authors have searched to gain insights by computing numerical estimates of the equilibria for some particular probability distributions of the...

Despite the lack of explicit formulas for the equilibrium of the first price auction in the general asymmetric setting, we obtain explicit expressions for the first order changes due to arbitrary deviations from the symmetric setting. From these expressions, we derive results of comparative...

There exists an explicit formula for the equilibrium strategies of the first price auction only in the symmetric case where the bidders’ valuations are distributed identically. The first price auction is considerably more difficult to investigate in the general case where the valuations may be...

If there is asymmetry among the bidders taking part in a first price auction, the equilibrium is not expost efficient. We consider a simple model of first price auction among two bidders where resale always occurs in case of inefficiency. We obtain mathematical formulas for the equilibrium...