Eliciting performance: deterministic versus proportional prizes

Abstract

Two standard schemes for awarding a prize have been examined in the literature. The prize is awarded $$(\pi _{D})$$ deterministically: to the contestant with the highest output; $$(\pi _{P})$$ probabilistically: to all contestants, with probabilities proportional to their outputs. Our main result is that if there is sufficient diversity in contestants’ skills, and not too much noise on output, then $$\pi _{P}$$ will elicit more output on average than $$\pi _{D}$$ . Indeed if contestants know each others’ skills (the complete information case) then the expected output at any Nash equilibrium selection under $$\pi _{P}$$ exceeds that at any individually rational selection under $$\pi _{D}$$ . If there is incomplete information, the inequality continues to hold when we restrict to Nash selections for both schemes.