Optimal Prize Allocation in Elimination Tournaments With Third Place Playoffs

This paper studies the optimal prize allocation in a standard elimination tournament augmented with a third-place playoff. Four heterogeneous players exert costly effort in order to advance in the competition and get a certain prize. The contest organizer, who aims at maximizing the total effort, is free to choose any prize allocation, subject to the feasibility constraint. We find that allocating the entire budget to the first-place reward is optimal if there is significant heterogeneity among the players. This induces the strongest competition in the final. This contribution is more significant than effort reduction in the semifinal. When there is a highlighted leader, a flat reward schedule with equal prizes becomes best. This can be explained by the fact that there is no significantly strong pair of the players. In this case, competition among the weak players contributes to the total effort the most.