Optimal Allocation of Multi-Dimensional Prizes in Contests with Heterogeneous Agents

Abstract

We develop a model where two players with asymmetric preferences engage in a contest game. The key novelty is the introduction of multi-dimensional rewards. We characterize the optimal prize allocation that maximizes aggregate effort. When heterogeneity in preferences is strong, the loser must get a positive reward, which is in stark contrast to the existing literature. Such allocation eliminates the advantage of the stronger competitor and incentivizes the opponent to exert more effort (the equilibrium effect). Applying the model to the data from professional tennis competitions, we show empirical evidence of such an equilibrium effect.

Keywords: contests, all-pay auctions, multi-dimensional prizes, heterogeneous players

JEL Classification: C72, D44, C51