Contests as Optimal Mechanisms under Signal Manipulation

We study the distribution of multiple homogeneous items to multiple agents with unit demand. Monetary transfer is not allowed and the allocation of the items can only depend on the informative signals that are manipulable by costly and wasteful efforts. Examples of such scenarios include grant allocation, college admission, lobbying and affordable housing. We show that the welfare-maximizing mechanism takes the form of a contest and characterize it. We apply our characterizations to study large contests. When the number of agents is large compared to item(s), the format of the optimal contest converges to winner-takes-all, but principal's payoff does not. When both the number of items and agents are large, allocation is randomized to middle types to induce no effort under optimal contest, which weakly decreases effort for all higher types.