STRATEGY-PROOF DIVISION WITH SINGLE-PEAKED PREFERENCES AND INDIVIDUALENDOWMENTS

We consider the problem of(re)allocating the total endowment of an inf initely divisible commodity among agents with single-peaked preference s and individual endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying Pareto opt imality, strategy-proofness, reversibility, and an equal-treatment con dition. The resulting rule turns out to be peaks-only and individually rational: the allocation assigned by the rule depends only on the pea ks of the preferences, and no agent is worse off than at his individua l endowment.