Convexity of Prize Sequences in Contests

This note studies contests in which multiple participants compete for two distinct prizes. The participants have distinct constant marginal costs, which are commonly known. We show that the contests have a unique Nash equilibrium, and we characterize the equilibrium payoffs and strategies in closed form. We also study how the convexity of the prize sequence, measured in the ratio of its first-order differences, affects the equilibrium payoffs and strategies. As an application, we simulate the convexity of the prize sequence that maximizes the asymmetric participants' total expected performance