Optimal prize allocation in contests: The role of negative prizes

In this paper, we analyze the role of negative prizes in contest design with a fixed budget, risk-neutral contestants, and independent private abilities. The effort-maximizing prize allocation rule features a threshold. When the highest effort is above the threshold, all contestants with lower efforts receive negative prizes. These negative prizes are used to augment the prize to the contestant with the highest effort, which better incentivizes contestants with higher abilities. When no contestant's effort exceeds the threshold, all contestants equally split the initial budget (or a portion of it) to ensure their participation. We find that allowing negative prizes can increase the expected total effort dramatically. In particular, if no bound is imposed on negative prizes, the expected total effort can be arbitrarily close to the highest possible effort inducible when all contestants have the maximum ability with certainty. The above contest is shown to be the optimal mechanism for a more general class of mechanisms.