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Population monotonicity in fair division of multiple indivisible goods

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  • Emre Doğan

    (National Research University Higher School of Economics)

Abstract

We consider the fair division of a set of indivisible goods where each agent can receive more than one good, and monetary transfers are allowed. We show that if there are at least three goods to allocate, no efficient solution is population monotonic (PM) on the superadditive Cartesian product preference domain, and the Shapley solution is not PM even on the submodular domain. Moreover, the incompatibility between efficiency and PM prevails in the case of at least four goods on the subadditive Cartesian product domain. We also show that in case there are only two goods to allocate, the Shapley solution and the constrained egalitarian solution are PM on the subadditive preference domain but not on the full preference domain. For the two-good case, we provide a new tool (the hybrid solutions) to construct efficient solutions that are PM on the entire monotone preference domain. The hybrid Shapley solution and the hybrid constrained egalitarian solution are two important examples of such solutions.

Suggested Citation

  • Emre Doğan, 2021. "Population monotonicity in fair division of multiple indivisible goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 361-376, June.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:2:d:10.1007_s00182-020-00749-7
    DOI: 10.1007/s00182-020-00749-7
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    1. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    2. Flip Klijn & Stef Tijs & Marco Slikker, 2001. "A Dual Egalitarian Solution," Economics Bulletin, AccessEcon, vol. 3(10), pages 1-8.
    3. Yves Sprumont, 2008. "Monotonicity and Solidarity Axioms in Economics and Game Theory," Studies in Choice and Welfare, in: Prasanta K. Pattanaik & Koichi Tadenuma & Yongsheng Xu & Naoki Yoshihara (ed.), Rational Choice and Social Welfare, pages 71-94, Springer.
    4. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401.
    5. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 153-169.
    6. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    7. William Thomson, 2007. "Cost allocation and airport problems," RCER Working Papers 537, University of Rochester - Center for Economic Research (RCER).
    8. Alkan, Ahmet, 1994. "Monotonicity and Envyfree Assignments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(4), pages 605-616, May.
    9. Hyungjun Kim, 2004. "Population monotonic rules for fair allocation problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 59-70, August.
    10. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    11. Moulin, Herve, 1992. "An Application of the Shapley Value to Fair Division with Money," Econometrica, Econometric Society, vol. 60(6), pages 1331-1349, November.
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