The optimal allocation of prizes in tournaments of heterogeneous agents

Tournaments are widely used in organizations, explicitly or implicitly, to reward the best-performing employees, e.g., through promotion or bonuses, and to punish the worst-performing employees, e.g., through firing or unfavorable job assignments. We use a principal-agent model to compare the efficiency of two tournament incentive schemes, reward tournament and punishment tournament, which, respectively, reward the best performer and punish the worst performer. We show that while the two schemes are equivalent when agents are symmetric in their ability, the equivalence is broken in the presence of heterogeneity. Specifically, punishment tournaments lead to higher profits of the firm. The reason is that low-ability agents are discouraged less in punishment tournaments than in reward tournaments, and hence can be compensated less to meet their participation constraints. Hence, our results predict that firms using punishment tournament contracts will perform better.