An algorithmic analysis of parallel contests

We consider two-stage parallel contests with a finite set of agents, as well as a finite set of heterogeneous contests with varying winning prizes. In the first stage, each agent simultaneously chooses in which contest he wants to compete, and in the second stage, the agents who chose the same contest compete against each other in a contest for a single prize. We first assume a general Tullock contest success function with nonlinear cost functions, and then we present an algorithm that converges to equilibrium, namely, the algorithm organizes the allocation of homogeneous or heterogeneous agents of two types, each with a different cost of effort, among the contests until no agent wishes to change his current contest. Later, we assume the Tullock contest success function with linear cost functions, and we show that for homogeneous agents, our model and a potential game are equivalent, allowing us to explicitly characterize the subgame perfect equilibrium with pure strategies.