The Allocation of a Prize

Consider agents who undertake costly effort to produce stochastic outputs observable by a principal. The principal can award a prize deterministically to the agent with the highest output or to all of them with probabilities that are proportional to their outputs. We show that the deterministic prize elicits more (expected, total) output when agents’ abilities are evenly matched, otherwise the proportional prize does better. Therefore if agents’ characteristics are sufficiently diverse compared to the noise on output, and are not heavily correlated (e.g., because they are picked i.i.d.), then the proportional prize will elicit more output. We in fact show that this is the case when any Nash selection (under the proportional prize) is compared with any individually rational strategy selection (under the deterministic prize), provided agents know each others’ characteristics (the complete information case). When there is incomplete information, the same conclusion holds (but now we must restrict to Nash selections for both prizes). In the event that the principal knows the distribution of agents’ characteristics, we also compute the optimal scheme for awarding the prize (among all schemes conceivable). JEL Classification: C70, C72, C79, D44, D63, D82. ∗Center for Game Theory, Department of Economics, Stony Brook University and Cowles Foundation for Research in Economics, Yale University †Department of Mathematics, Rutgers University, New Brunswick, New Jersey