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...

We study contests where several privately informed agents bid for a prize. All bidders bear a cost of bidding that is an increasing function of their bids, and, moreover, bids may be capped. We show that regardless of the number of bidders, if bidders have linear or concave cost functions, then...