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

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 and the designer cannot assign identity-dependent prizes, the loser must get a positive reward. This 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. Using data from four professional tennis competitions where prizes include money and the ATP ranking points, we propose a structural estimator and recover contestants skill-preference profiles. The identification strategy relies on exogenous variation in monetary and non-monetary prizes and the random matching between players in the first round. We show that both reward items shape individual incentives to compete. Our counterfactual experiments reveal that for some skill-preference profiles, the increase in first-round monetary losing rewards can indeed improve the aggregate effort