  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.
