We prove that, around the symmetric case, where the values are identically distributed, the equilibrium of the first price auction is jointly differentiable with respect to general bidder-specific parameters of the value distributions. We show that the revenue equivalence between the first-price...

If the value cumulative distribution functions are log-concave at the highest lower extremity of their supports of the first-price auction in the asymmetric indepent private values model.

In the independent-private-value model, we allow resale among bidders following a first-price sealed-bid, second-price sealed-bid, or English auction with two bidders. We consider two regimes with regard to the disclosure of the sealed bids: full disclosure and no disclosure. Either the auction...

If the value cumulative distribution functions are log-concave at the highest lower extremity of their supports, a simple geometric argument establishes the uniqueness of the equilibrium of the first-price auction in the asymmetric independent private value model.

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...

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...

We add a resale stage to standard auctions with two bidders. Bids are either kept secret or made public. Either the auction winner or the auction loser chooses the resale price. We characterize an infinity of equilibria of the second-price auction and a unique equilibrium of the first-price...

We deviate from the symmetric case of the independent private value model by allowing the bidders’ value distributions, which depend on parameters, to be slightly different. We show that previous results about the equality to the first-order in the parameters between revenues from the...