Fraud-proof non-market allocation mechanisms

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Abstract:  We study the optimal design of fraud-proof allocation mechanisms in settings without transfers (public housing, vaccines, disaster relief) and characterize planner-optimal mechanisms under different fraud technologies. By incorporating the resource and quota constraints with Lagrange multi- pliers we reduce the planner’s problem into one that is separable across demographic groups. The multipliers determine group-specific eligibility thresholds wˆi and lead to an endogenous prioritization of groups. We solve the “within” group problem for different classes of falsification technolo- gies. Theorem 1 characterizes the planner-optimal fraud-proof mechanism for cost functions that satisfy upward increasing differences, UID, whereasTheorem 2 provides the same characterization for upward decreasing dif- ferences UDD. Under UDD costs, local falsification-proofness constraints,FPIC, bind and we rely on a first-order approach to derive an optimal within group assignment; under UID costs, FPIC bind non-locally. We solve this problem by building an auxiliary problem which turns out to be the dual of the famous Monge-Kantorovich transportation problem. Optimal rules typically do not assign objects to agents with very low social scores, involve randomization for intermediate scores and assign an object with certainty to high scores.

Methodologically, our analysis suggests a way of tackling problems of mechanism design without transfers and costly fraud that highlights novel connections to the literature of optimal transportation theory

Joint with Eduardo Perez-Richet