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Nash Implementation in an Allocation Problem with Single-Dipped Preferences

  • Ahmed Doghmi

    ()

    (National Institute of Statistics and Applied Economics, Madinat Al Irfane, Rabat Institutes, 10100 Rabat, Morocco
    University of Caen, Center for Research in Economics and Management(UMR CNRS 6211), 19 Rue Claude Bloch 14032 Caen, Cedex, France)

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    In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic ( but they do not satisfy no-veto power) and hence Nash implementable.

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    Article provided by MDPI, Open Access Journal in its journal Games.

    Volume (Year): 4 (2013)
    Issue (Month): 1 (January)
    Pages: 38-49

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    Handle: RePEc:gam:jgames:v:4:y:2013:i:1:p:38-49:d:23225
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    1. Lombardi, Michele & Yoshihara, Naoki, 2012. "Natural Implementation with Partially Honest Agents," Discussion Paper Series 561, Institute of Economic Research, Hitotsubashi University.
    2. Lars Ehlers, 2002. "Probabilistic allocation rules and single-dipped preferences," Social Choice and Welfare, Springer, vol. 19(2), pages 325-348.
    3. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    4. 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 14, September.
    5. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    6. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
    7. 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.
    8. Hitoshi Matsushima, 2007. "Behavioral Aspects of Implementation Theory," CIRJE F-Series CIRJE-F-523, CIRJE, Faculty of Economics, University of Tokyo.
    9. Salvador Barberà & Dolors Berga & and Bernardo Moreno, 2009. "Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences," Working Papers 418, Barcelona Graduate School of Economics.
    10. Ville Korpela, 2014. "Bayesian implementation with partially honest individuals," Social Choice and Welfare, Springer, vol. 43(3), pages 647-658, October.
    11. Hitoshi Matsushima, 2007. "Role of Honesty in Full Implementation," CIRJE F-Series CIRJE-F-518, CIRJE, Faculty of Economics, University of Tokyo.
    12. 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.
    13. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
    14. Ahmed Doghmi & Abderrahmane ZIAD, 2012. "On Partial Honesty Nash Implementation," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201201, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    15. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    16. Ziad, Abderrahmane, 1997. "On the necessary and sufficient conditions for Nash implementation," Economics Letters, Elsevier, vol. 56(2), pages 209-213, October.
    17. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Reexamination of Maskin's Theorem on Nash implementability," Economics Letters, Elsevier, vol. 100(1), pages 150-152, July.
    18. Ziad, Abderrahmane, 1998. "A new necessary condition for Nash implementation," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 381-387, May.
    19. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    20. Dutta, Bhaskar & Sen, Arunava, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," Review of Economic Studies, Wiley Blackwell, vol. 58(1), pages 121-28, January.
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