Carrots and Sticks: Prizes and Punishments in Contests

We study optimal contest design in situations where the designer can reward high performance agents with positive prizes and punish low performance agents with negative prizes. We link the optimal prize structure to the curvature of distribution of abilities in the population. In particular, we identify conditions under which, even if punishment is costly, punishing the bottom is more effective than rewarding the top in eliciting effort input . If punishment is costless, we study the optimal number of punishments in the contest. J C : D44, D82, J31, J41. K : Contests, All-pay auctions, Punishments, Order Statistics. ∗Moldovanu: Department of Economics, University of Bonn, Lennestr. 37, 53113 Bonn, Germany; e-mail: [email protected]. Sela: Department of Economics, Ben Gurion University, Beer Sheva 84105, Israel; e-mail: [email protected]. Shi: Department of Economics, University of Toronto, 150 St. George Street, Toronto, ON M5S 3G7, Canada; e-mail: [email protected].