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Nash implementing social choice rules with restricted ranges

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  • M. Remzi Sanver

    () (Université Paris-Dauphine)

Abstract

Abstract We consider Nash implementation of social choice rules with restricted ranges, i.e., where some of the available alternatives are chosen at no preference profile. We show that the appropriate adaptation of Maskin monotonicity to this context depends on the range of the mechanisms: the wider is this range, the weaker is the monotonicity condition to be used. As a result, mechanisms employing outcome functions which allow for out-of-range alternatives at off-equilibrium messages can Nash implement social choice rules which fail to be Nash implementable by mechanisms whose ranges are restricted to the range of the social choice rule to be implemented. The Walrasian social choice correspondence is a particular instance of this. Moreover, social choice rules which are not Maskin monotonic can be “monotonized” by the addition of artificial out-of-range alternatives—a point we illustrate through Solomon’s Dilemma.

Suggested Citation

  • M. Remzi Sanver, 2017. "Nash implementing social choice rules with restricted ranges," Review of Economic Design, Springer;Society for Economic Design, vol. 21(1), pages 65-72, March.
  • Handle: RePEc:spr:reecde:v:21:y:2017:i:1:d:10.1007_s10058-016-0195-z
    DOI: 10.1007/s10058-016-0195-z
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    References listed on IDEAS

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    1. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
    2. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    3. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-1593, November.
    4. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
    5. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    6. M. Sanver, 2006. "Nash implementing non-monotonic social choice rules by awards," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 453-460, June.
    7. Benoit, Jean-Pierre & Ok, Efe A., 2006. "Maskin's Theorem with limited veto power," Games and Economic Behavior, Elsevier, vol. 55(2), pages 331-339, May.
    8. Orhan Erdem & M. Sanver, 2005. "Minimal monotonic extensions of scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 31-42, October.
    9. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
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    More about this item

    Keywords

    Maskin monotonicity; Nash implementation; Range restrictions; Walrasian solution; Solomon’s Dilemma;

    JEL classification:

    • D79 - Microeconomics - - Analysis of Collective Decision-Making - - - Other

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