First Price Auctions with Participation Costs∗

This paper studies equilibria of first price auctions with participation costs in the independent private values environment. We focus on the cutoff strategies in which each bidder participates and submits a bid if his value is greater than or equal to a critical value, the cutoff point. It is shown that, when bidders are homogenous, there always exists a symmetric equilibrium, and further, that the equilibrium is unique for concave valuation distribution functions. There also exists an asymmetric equilibrium when the distribution function is strictly convex. We find that concavity and strict convexity play a similar role for the uniqueness and multiplicity of equilibria when bidders are heterogenous in valuation distribution functions. Journal of Economic Literature Classification Number: C62, C72, D44, D61, D82.