Asymmetric first price auctions

We propose a new approach to asymmetric …rst price auctions which circumvents having to directly examine bidding strategies. Speci…cally, the ratio of bidders’payo¤s is compared to the ratio of the distribution functions that describe beliefs. This comparison allows a number of easy inferences. In the existing theoretical literature, assumptions of …rst order stochastic dominance or stronger imply that the latter ratio has very speci…c properties. Most existing results therefore follow as simple corollaries from our two main results. We prove that …rst order stochastic dominance is necessary for bidding strategies not to cross. When this assumption is relaxed in the numerical literature it is done in a manner that leads to exactly one crossing. We construct examples with several crossings. General results are provided for types of asymmetry not studied before, including second order stochastic dominance. In this case, the bid distributions will cross in auctions with two bidders. JEL Classi…cation Numbers: C72, D44, D82.