On the analysis of asymmetric first price auctions

We provide new tools for studying asymmetric first price auctions, connecting their equilibria to the ρ-concavity of the underlying type distributions, and showing how one can use surplus expressions for symmetric auctions to bound equilibrium behavior in asymmetric auctions. We apply these tools to studying procurement auctions in which, as is common in practice, one seller is given an advantage, reflecting for example better reliability or quality. We show conditions under which for any given first price handicap auction, there exists a superior second price auction with bonuses.