A first price auction with an arbitrary number of asymmetric bidders

Abstract: We examine an auction setting with private values and n ≥ 2 bidders, which differ in the probability to have a low (high) value. We prove that for the first price auction, the equilibrium strategies can be written in closed form and there are gaps in the equilibrium bid distribution of each bidder except the strongest two. Our equilibrium characterization allows to prove that in this setting the seller prefers the second price auction to the first price auction for each n ≥ 2.