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Nash Implementation in Rationing Problems with Single-Crossing Preferences

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  • Doghmi Ahmed

    (University of Rabat, Mohammadia School of engineering, the QSM Laboratory, Avenue Ibnsina B. P. 765 Agdal, 10100 Rabat, Morocco; and University of Caen, Center for Research in Economics and Management (UMR CNRS 6211), 19 Rue Claude Bloch 14032 Caen, Cedex, France; and National Institute of Statistics and Applied Economics, Madinat Al Irfane, Rabat Institutes, 10100 Rabat, Morocco)

Abstract

In this paper we study the rationing problems in using the issue of Nash implementation in an environment of single-crossing preferences. We show that strict monotonicity (i) implies strict weak no-veto power and unanimity and (ii) is equivalent to Maskin monotonicity, which is vacuously checked in this domain. We show that any social choice correspondence that has full range can be implemented in Nash equilibria.

Suggested Citation

  • Doghmi Ahmed, 2014. "Nash Implementation in Rationing Problems with Single-Crossing Preferences," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 1-6, July.
    • Handle: RePEc:bpj:maecol:v:1:y:2014:i:2-4:p:6:n:4
    DOI: 10.1515/mel-2013-0019
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    References listed on IDEAS

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    1. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    2. Doghmi Ahmed & Ziad Abderrahmane, 2013. "On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 1-14, September.
    3. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    4. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
    5. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    6. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Reexamination of Maskin's Theorem on Nash implementability," Economics Letters, Elsevier, vol. 100(1), pages 150-152, July.
    7. Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 275-298, February.
    8. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745.
    9. Thomson, W., 1990. "Monotonic And Consistent Solutions To The Problem Of Fair Allocation When Preferences Are Single-Peaked," RCER Working Papers 231, University of Rochester - Center for Economic Research (RCER).
    10. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    11. Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    12. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
    13. Klaus, Bettina, 2001. "Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object," Games and Economic Behavior, Elsevier, vol. 34(1), pages 64-82, January.
    14. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
    15. Doghmi Ahmed, 2013. "Nash Implementation in Private Good Economies when Preferences are Single-Dipped with Best Indifferent Allocations," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 35-42, October.
    16. Ahmed Doghmi & Abderrahmane Ziad, 2013. "Nash Implementation in Private Good Economies with Single-Plateaued Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201311, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    17. David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 491-514, June.
    18. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
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