Sorted or pooled? Optimal tournament design for heterogeneous contestants

Abstract

The optimal tournament for the heterogeneous contestants is described and developed in approach of game theory, which includes the sorted tournament between the strong contestants with high ability, the sorted tournament between the weak contestants with low ability, and the pooled tournament between the strong and the weak contestants. By comparing the equilibrium results of the incentive structure, the efforts level, and the expected profits in each kind of tournament, it is found that the strong contestants can get more utilities in the pooled tournament, and hence prefer to take part in the pooled tournament to compete with the weak competitors, while the weak contestants only can get the reservation utility in both the sorted and pooled tournament, and hence do not care about the abilities of competitors. The principal will choose and implement the sorted tournament because he can acquire more profits than that in the pooled tournament.