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An Application of the Shapley Value to Fair Division with Money

Herve Moulin

Abstract

We consider the fair division of unproduced goods when monetary compensations are feasible and utilities are quasi-linear. Under efficiency, the four axioms: individual rationality, resource monotonicity, population solidarity, and stand alone test, show little compatibility. However when the goods have enough substitutability in everyone's preferences, the Shapley value of the surplus sharing game satisfies all four axioms. An example is the optimal assignment of indivisible goods when every agent consumes only one good.