The n-Player Hirshleifer Contest

Abstract

We characterize the equilibrium set of the n-player Hirshleifer contest with homogeneous valuations. A symmetric equilibrium always exists. It necessarily corresponds to multilateral peace for su¢ cient noise and uses …nitesupport randomized strategies otherwise. Asymmetric equilibria are feasible for n 3 contestants only, and only for su¢ ciently small noise. In pure strategies, any asymmetric equilibrium corresponds to one-sided dominance, but there is also a variety of payo¤-inequivalent mixed-strategy equilibria for small noise. For arbitrarily small noise, at least two contestants engage in cut-throat competition, while any others become ultimately inactive. Of some conceptual interest is the observation that, for n su¢ ciently large, the unique equilibrium is multilateral peace.