The impossibility of strategy-proof, Pareto efficient, and individually rational rules for fractional matching

Abstract For a model of fractional matching, interpreted as probabilistic matching, together with the allocation of non-negative amounts of money, we show that strategy-proofness, ex post Pareto efficiency of the matching, and a weak version of ex ante individual rationality are incompatible when each agent's utility is a linear function of both their fractional assignment and money. We identify some avenues to escape this impossibility.

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