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, 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). Using data from twelve professional tennis competitions where prizes include money and the ATP ranking points, we test our theoretical predictions empirically. The identification strategy relies on exogenous variation in prizes over both dimensions and random matching between the players. We document the equilibrium effect in the data and recover the underlying preference profiles that define its direction