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/or to punish the worst-performing employees, e.g., through firing or unfavorable job assignments. We explore the impact of the allocation of prizes on the effectiveness of tournament incentive schemes. We show that while multiple prize allocation rules are equivalent when agents are symmetric in their ability, the equivalence is broken in the presence of heterogeneity. Under a wide range of conditions, punishment tournaments, i.e., tournaments that award a low prize to relatively few bottom performers, are optimal for the firm. The reason is that low-ability agents are discouraged less in punishment tournaments, and hence can be compensated less to meet their participation constraints.