Allocating Resources under Strategic Misrepresentation

We study how to allocate resources to participants who can strategically misrepresent their deservingness at a cost. A principal assigns item(s) (or money) among multiple agents on the basis of their costly signals. Each agent's signal reflects their private type in the absence of misrepresentation but can be inflated above their true type at a cost. The principal is a social planner who aims to maximize the weighted average of matching efficiency and a utilitarian objective. Strategic misrepresentation introduces novel incentive-compatibility constraints, under which we characterize the optimal mechanism. We apply our characterization to two kinds of markets, distinguished by resource scarcity, and show that the principal strictly benefits from randomizing the allocations based on costly signals when the population of participants is large enough. Interestingly, in large markets with scarce resources, the format of the optimal mechanism converges to a winner-takes-all contest; however, there is a non-diminishing value in randomizing allocations to middle types as the population of participants grows.