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The B.E. Journal of Theoretical Economics

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On Nash Implementability in Allotment Economies under Domain Restrictions with Indifference

Ahmed Doghmi
  • Corresponding author
  • University of Rabat, Mohammadia School of Engineering, the QSM Laboratory, Avenue Ibn Sina B.P. 765 Agdal, 10100 Rabat, Morocco
  • Center for Research in Economics and Management (UMR CNRS 6211), University of Caen, 19 Rue Claude Bloch 14032 Caen, Cedex, France
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Published Online: 2016-06-01 | DOI: https://doi.org/10.1515/bejte-2015-0091


In this paper we give a full characterization of Nash implementability of social choice correspondences (SCCs) in allotment economies on preference domains with private values and different types of indifference. We focus on single-peaked/single-plateaued preferences with worst indifferent allocations, single-troughed preferences and single-troughed preferences with best indifferent allocations. We begin by introducing a weak variant of no-veto power, called I-weak no-veto power, which form together with unanimity and a stronger version of Maskin monotonicity a sufficient condition for Nash implementation in general environment. We apply this result to the above preference domains and we prove that any SCC that has full range is Nash implementable if and only if it satisfies Maskin monotonicity. We examine the implementability of some well-known correspondences. We give examples of SCCs that are monotonic in the unrestricted domains and also monotonic in our setup, and we provide exemples of SCCs that are not monotonic in the unrestricted domains, but monotonic and therefore Nash implementable in our context. Finally, we give examples of SCCs that are not monotonic in the restricted domains and also not monotonic in our area, and therefore not Nash implementable.

Keywords: allotment economies; domain restrictions with indifference; nash implementation

JEL: C72; D71


  • Aragón, G. -A., and D. -M. Caramuta. 2011. Single-Dipped Preferences with Indifferences: Strong Group Strategy-Proof and Unanimous Social Choice Functions. Working Paper, Universitat Autnoma De Barcelona.

  • Barberà, S. 2007. “Indifferences and Domains Restrictions.” Analysis and Kritik 29:146–62.Google Scholar

  • Berga, D. 1998. “Strategy-Proofness and Single-Plateaued Preferences.” Mathematical Social Sciences 35:105–20.CrossrefGoogle Scholar

  • Berga, D., and B. Moreno. 2009. “Strategic Requirements with Indifference: Single-Peaked Versus Single-Plateaued Preferences.” Social Choice and Welfare 32:275–98.CrossrefWeb of ScienceGoogle Scholar

  • Berga, D. 2006. “A Note on Strategy-Proofness and Single-Plateaued Preferences.” Working paper.

  • Bossert, W., and H. Peters. 2013. “Single-Plateaued Choice.” Mathematical Social Sciences 66:134–9.Web of ScienceCrossrefGoogle Scholar

  • Bossert, W., and H. Peters. 2014. “Single-Basined Choice.” Journal of Mathematical Economics 52:162–168.CrossrefWeb of Science

  • Cantala, D. 2004. “Choosing the Level of a Public Good When Agents Have an Outside Option.” Social Choice and Welfare 22:491–514.CrossrefGoogle Scholar

  • Dasgupta, P., P. Hammond, and E. Maskin. 1979. “The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility.” Review of Economic Studies 46:181–216.Crossref

  • Danilov, V. 1992. “Implementation via Nash Equilibrium.” Econometrica 60:43–56.CrossrefGoogle Scholar

  • Diss, M., A. Doghmi, and A. Tlidi. 2015. “Strategy Proofness and Unanimity in Private Good Economies with Single-Peaked Preferences.” Working paper N° 1528, GATE Lyon Saint-Etienne, available at SSRN 2688465.

  • Doghmi, A. 2013a. “Nash Implementation in an Allocation Problem with Single-Dipped Preferences.” Games 4:38–49.CrossrefGoogle Scholar

  • Doghmi, A. 2013b. “Nash Implementation in Private Good Economies When Preferences Are Single-Dipped with Best Indifferent Allocations.” Mathematical Economics Letters 1:35–42.CrossrefGoogle Scholar

  • Doghmi, A., and A. Ziad. 2008a. “Reexamination of Maskin’s Theorem on Nash Implementability.” Economics Letters 100:150–2.Web of ScienceCrossrefGoogle Scholar

  • Doghmi, A., and A. Ziad. 2008b. “Nash Implementation in Exchange Economies with Singlepeaked Preferences.” Economics Letters 100:157–60.CrossrefGoogle Scholar

  • Doghmi, A., and A. Ziad. 2013a. “On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition.” The B.E. Journal of Theoretical Economics 13:1–14.Google Scholar

  • Doghmi, A., and A. Ziad. 2013b. “Nash Implementation in Private Good Economies with Single-Plateaued Preferences.” Working paper.

  • Doghmi, A., and A. Ziad. 2015. “Nash Implementation in Private Good Economies with Single-Plateaued Preferences and in Matching Problems.” Mathematical Social Sciences 73:32–9.Web of ScienceCrossrefGoogle Scholar

  • Doğan, B. 2015. “Nash-Implementation of the No-Envy Solution on General Domains of Economies.” Working paper, available at SSRN 2637965.

  • Dutta, B., and A. Sen. 1991. “A Necessary and Sufficient Condition for Two-Person Nash Implementation.” Review of Economic Studies 58:121–8.CrossrefGoogle Scholar

  • Ehlers, L. 2002. “Probabilistic Allocation Rules and Single-Dipped Preferences.” Social Choice and Welfare 19:325–48.CrossrefGoogle Scholar

  • Foley, D. 1967. “Resource Allocation and the Public Sector.” Yale Economic Essays 7:45–98.Google Scholar

  • Gaertner, W. 2001. Domain Conditions in Social Choice Theory. Cambridge, United Kingdom: Cambridge, University Press.Google Scholar

  • Inada, K. I. 1964. “A Note on the Simple Majority Decision Rule.” Econometrica 32:525–31.CrossrefGoogle Scholar

  • Klaus, B., and O. Bochet. 2013. “The Relation Between Monotonicity and Strategy-Proofness.” Social Choice and Welfare 40:41–63.Web of ScienceCrossrefGoogle Scholar

  • Manjunath, V. 2011. “Strategic and Normative Analysis of Ressource Allocation Problems.” Phd. thesis, University of Rechester, New York.Google Scholar

  • Maskin, E. 1999. “Nash Equilibrium and Welfare Optimality. M.I.T. Mimeo, 1977.” Published 1999 in the Review of Economic Studies 66:23–38.Google Scholar

  • Moore, J., and R. Repullo. 1990. “Nash Implementation: A Full Characterization.” Econometrica 58:1083–100.CrossrefGoogle Scholar

  • Moulin, H., 1984. “Generelized Condorcet-Winners for Single-Peaked and Single-Plateau Preferences.” Social Choice and Welfare 1:127–147.Crossref

  • Sjöström, T. 1991. “On the Necessary and Sufficient Conditions for Nash Implementation.” Social Choice and Welfare 8:333–40.CrossrefGoogle Scholar

  • Thomson, W. 1990. “Manipulation and Implementation to Solutions to the Problem of Fair Allocations when Preferences are Single-Peaked.” mimeo, University of Rochester.

  • Thomson, W. 2010. “Implementation to Solutions to the Problem of Fair Allocations When Preferences Are Single-Peaked.” Review of Economic Design 14:1–15.CrossrefGoogle Scholar

  • Yamato, T. 1992. “On Nash Implementation of Social Choice Correspondences.” Games and Economic Behavior 4:484–92.CrossrefGoogle Scholar

  • Ziad, A. 1997. “On the Necessary and Sufficient Conditions for Nash Implementation.” Economics Letters 56:209–13.CrossrefGoogle Scholar

  • Ziad, A. 1998. “A New Necessary Condition for Nash Implementation.” Journal of Mathematical Economics 29:381–7.CrossrefGoogle Scholar

About the article

Published Online: 2016-06-01

Published in Print: 2016-06-01

Citation Information: The B.E. Journal of Theoretical Economics, Volume 16, Issue 2, Pages 767–795, ISSN (Online) 1935-1704, ISSN (Print) 2194-6124, DOI: https://doi.org/10.1515/bejte-2015-0091.

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