Optimality of Winner-Take-All Contests: The Role of Attitudes toward Risk

Résumé

It has been established in the literature that, under the assumption of risk-neutral contestants, it is usually optimal for an effort-maximizing contest organizer with a fixed prize budget to award everything to a single winner. This paper studies the role of risk attitudes – risk aversion and prudence in particular – in determining the optimality of winner-take-all contests. We compare the typical single-winner lottery contest with two alternative ways of spreading the rewards to more players: through holding multiple prize-giving lottery competitions or through guaranteeing a bottom prize for the losers. In the first comparison, we found that the multiple-competition contest is as effective as the winner-take-all contest when the contestants are risk neutral, but the former induces more effort than the latter when the contestants are both risk averse and prudent. In the second comparison, we found that the contest with a bottom prize is always dominated by the winner-take-all contest when the contestants are risk neutral, but the former could have an advantage over the latter when the contestants are both risk averse and prudent, and it is more likely so as the contestants become more prudent.

Mots-clés

contests; winner take all; multiple prizes; risk aversion; prudence;

Codes JEL

C72: Noncooperative Games
D72: Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior
D81: Criteria for Decision-Making under Risk and Uncertainty