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Nash Implementation in Private Good Economies with Single-Plateaued Preferences

  • Ahmed Doghmi

    (National Institute of Statistics and Applied Economics of Rabat, Morocco)

  • Abderrahmane Ziad

    (Normandie University, Caen, Faculty of Economics and Business Administration - CREM CNRS UMR6211, France)

Abstract: In this paper we explore the problem of Nash implementation providing new sufficient conditions called I-monotonicity and I-weak no-veto power. Firstly, we show that these conditions together with unanimity are sufficient for the implementation of social choice correspondences (SCCs) in Nash equilibria. Secondly, we prove that, in the domain of the private good economies with single-plateaued preferences, a solution of the problem of fair division is Nash implementable if and only if it satisfies Maskin monotonicity. We provide examples of SCCs satisfying or not Maskin monotonicity.

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Paper provided by Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS in its series Economics Working Paper Archive (University of Rennes 1 & University of Caen) with number 201311.

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Date of creation: Apr 2013
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Handle: RePEc:tut:cremwp:201311
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  1. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
  2. Hitoshi Matsushima, 2007. "Role of Honesty in Full Implementation," CIRJE F-Series CIRJE-F-518, CIRJE, Faculty of Economics, University of Tokyo.
  3. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Reexamination of Maskin's Theorem on Nash implementability," Economics Letters, Elsevier, vol. 100(1), pages 150-152, July.
  4. Dolors Berga & Bernardo Moreno, 2008. "Strategic Requirements with Indifference: Single-Peaked versus Single-Plateaued Preferences," Working Papers 2008-7, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
  5. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
  6. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," Discussion Paper Series 555, Institute of Economic Research, Hitotsubashi University.
  7. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
  8. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
  9. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  10. 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.
  11. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
  12. Matsushima, Hitoshi, 2008. "Behavioral aspects of implementation theory," Economics Letters, Elsevier, vol. 100(1), pages 161-164, July.
  13. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  14. Lars Ehlers, 2002. "Strategy-proof allocation when preferences are single-plateaued," Review of Economic Design, Springer, vol. 7(1), pages 105-115.
  15. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
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