Equilibria and comparative statics in two-player contests

We analyze two-player contests in which each player exerts effort to influence his probability of winning the prize. Assuming the contest success function is homogeneous of degree zero, we characterize Nash equilibria, provide conditions for existence of a pure-strategy equilibrium, and present comparative statics results. For comparative statics, we consider the dependence of equilibrium efforts, success probabilities, and expected payoffs on players' values for the prize. We also analyze the effects on the comparative statics of relaxing the homogeneity assumption. These findings extend previous results based on more restricted forms of the contest success function.