The Optimal Rewards in Contests

We study all-pay contests under incomplete information where the reward is a func- tion of the contestant's type and also of his effort. We analyze the optimal reward for the designer when the reward is either multiplicatively separable or additively separable in effort and type. In the multiplicatively separable environment the optimal reward is always positive while in the additively separable environment it may also be negative. In both environments, depending on the designer's utility, the optimal reward may either increase or decrease in the contestants' effort. Finally, in both environments, the designer's payoff depends only upon the expected value of the effort-dependent rewards and not the number of rewards.