Competition among Parallel Contests

We investigate the model of multiple contests held in parallel, where each contestant selects one contest to join and each contest designer decides the prize structure to compete for the participation of contestants. We first analyze the strategic behaviors of contestants and completely characterize the symmetric Bayesian Nash equilibrium. As for the strategies of contest designers, when other designers' strategies are known, we show that computing the best response is NP-hard and propose a fully polynomial time approximation scheme (FPTAS) to output the $\epsilon$-approximate best response. When other designers' strategies are unknown, we provide a worst case analysis on one designer's strategy. We give an upper bound on the utility of any strategy and propose a method to construct a strategy whose utility can guarantee a constant ratio of this upper bound in the worst case.