Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results

Abstract

This paper studies contests in which three or more players compete for two nonidentical prizes. The players have distinct constant marginal costs of performance or bid, which are commonly known. We show that the contests have a generically unique Nash equilibrium, and it is in mixed strategies. Moreover, we characterize the equilibrium payoffs and strategies in closed form. We also study how the equilibrium payoffs and strategies vary with the prizes. As an application, we numerically compute the optimal allocation of prizes that maximizes the total expected bid of asymmetric players.