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An Application of the Shapley Value to Fair Division with Money

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  • Moulin, Herve

Abstract

The author considers fair division when monetary compensations are feasible and utilities are quasi-linear. Four axioms are discussed: individual rationality, resource monotonicity, population solidarity, and the stand alone test. The latter views the utility from consuming all the goods as an upper bound on every coalition's actual (joint) utility. Under efficiency, the four axioms 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. Copyright 1992 by The Econometric Society.

Suggested Citation

  • Moulin, Herve, 1992. "An Application of the Shapley Value to Fair Division with Money," Econometrica, Econometric Society, vol. 60(6), pages 1331-1349, November.
  • Handle: RePEc:ecm:emetrp:v:60:y:1992:i:6:p:1331-49
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    Cited by:

    1. Sanchez, Francisco Sanchez, 2002. "About inheritance distribution," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 297-309, July.
    2. de Clippel, Geoffroy & Bejan, Camelia, 2011. "No profitable decompositions in quasi-linear allocation problems," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1995-2012, September.
    3. Helm, Carsten & Simonis, Udo E., 2000. "Distributive justice in international environmental policy - theoretical foundation and exemplary formulation," Discussion Papers, Research Professorship Environmental Policy FS II 00-404, Social Science Research Center Berlin (WZB).
    4. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    5. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506 Elsevier.
    6. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation," Working Papers 33, Barcelona Graduate School of Economics.
    7. Böhringer, Christoph & Helm, Carsten, 2001. "Fair division with general equilibrium effects and international climate politics," ZEW Discussion Papers 01-67, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    8. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    9. Bevia, Carmen, 1996. "Population monotonicity in economies with one indivisible good," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 125-137, October.
    10. Victor Aguiar & Roland Pongou & Jean-Baptiste Tondji, 2016. "Measuring and Decomposing the Distance to the Shapley Wage Function with Limited Data," Working Papers 1613e, University of Ottawa, Department of Economics.
    11. Miguel Gines & Francisco Marhuenda, 1996. "Cost monotonic mechanisms," Investigaciones Economicas, Fundación SEPI, vol. 20(1), pages 89-103, January.
    12. Geoffroy de Clippel, 2010. "Copmment on Egalitarianism under Incomplete Information," Working Papers 2010-4, Brown University, Department of Economics.
    13. Böhringer, Christoph & Helm, Carsten, 2008. "On the fair division of greenhouse gas abatement cost," Resource and Energy Economics, Elsevier, vol. 30(2), pages 260-276, May.
    14. Massimo Marinacci & Luigi Montrucchio, 2005. "Ultramodular Functions," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 311-332, May.
    15. Kazuhiko Hashimoto & Yu Nakayama, 2016. "Strategy-Proofness on Bankruptcy Problems with an Indivisible Object," ISER Discussion Paper 0961, Institute of Social and Economic Research, Osaka University.
    16. Helm, Carsten & Simonis, Udo E., 2000. "Verteilungsgerechtigkeit in der internationalen Umweltpolitik: Theoretische Fundierung und exemplarische Formulierung," Discussion Papers, Research Professorship Environmental Policy FS II 00-403, Social Science Research Center Berlin (WZB).
    17. Debasis Mishra & Bharath Rangarajan, 2007. "Cost sharing in a job scheduling problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 369-382, October.
    18. Eve Ramaekers, 2013. "Fair allocation of indivisible goods: the two-agent case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 359-380, July.
    19. Bevia, Carmen, 1996. "Population monotonicity in a general model with indivisible goods," Economics Letters, Elsevier, vol. 50(1), pages 91-97, January.

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