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Nash-implementation of the no-envy solution on symmetric domains of economies

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  • Doğan, Battal

Abstract

We show that a simple game form, which resembles the “Divide-and-Choose” procedure, Nash-implements the no-envy solution on domains of economies where the set of feasible allocations is symmetric (an allocation obtained from a feasible allocation by interchanging the bundles of any two agents is also feasible) and preferences are complete (each agent can compare any two bundles). Our result extends a result by Thomson (2005) and it is applicable to a wide class of models including the classical model of fair allocation, the unidimensional single-peaked model, cake division model, and allocation of indivisible objects with monetary transfers. We show that, even when the preferences exhibit consumption externalities, an extension of the no-envy solution is Nash-implementable on general domains of economies.

Suggested Citation

  • Doğan, Battal, 2016. "Nash-implementation of the no-envy solution on symmetric domains of economies," Games and Economic Behavior, Elsevier, vol. 98(C), pages 165-171.
    • Handle: RePEc:eee:gamebe:v:98:y:2016:i:c:p:165-171
    DOI: 10.1016/j.geb.2016.06.010
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    References listed on IDEAS

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    1. Cloutier, John & Nyman, Kathryn L. & Su, Francis Edward, 2010. "Two-player envy-free multi-cake division," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 26-37, January.
    2. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    3. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 1-15, March.
    4. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
    5. Gabrielle Demange & Ahmet Alkan & David Gale, 1991. "Fair Allocation of Indivisible Goods and Money and Criteria of Justice," Post-Print halshs-00670945, HAL.
    6. Fleurbaey, Marc & Maniquet, Francois, 1996. "Fair allocation with unequal production skills: The No Envy approach to compensation," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 71-93, August.
    7. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    8. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    9. Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    10. Kutlu, Levent, 2008. "Intersection of Nash implementable social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 255-257, March.
    11. Benoit, Jean Pierre & Ok, Efe A. & Sanver, M. Remzi, 2007. "On combining implementable social choice rules," Games and Economic Behavior, Elsevier, vol. 60(1), pages 20-30, July.
    12. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    13. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1996. "Toward Natural Implementation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 949-980, November.
    14. William Thomson, 2007. "Children Crying at Birthday Parties. Why?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 501-521, June.
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    More about this item

    Keywords

    No-envy; Nash-implementation; Divide-and-Transpose;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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