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A solution to the two-person implementation problem

Author

Listed:
  • Jean-François Laslier

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Matías Núñez

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, GENES - Groupe des Écoles Nationales d'Économie et Statistique)

  • M. Remzi Sanver

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose strike mechanisms as a solution to the classical problem of Hurwicz and Schmeidler (1978) and Maskin (1999) according to which, in two-person societies, no Pareto efficient rule is Nash-implementable. A strike mechanism specifies the number of alternatives that each player vetoes. Each player simultaneously casts these vetoes and the mechanism selects randomly one alternative among the non-vetoed ones. For strict preferences over alternatives and under a very weak condition for extending preferences over lotteries, these mechanisms are deterministic-in-equilibrium. They Nash implement a class of Pareto efficient social choice rules called Pareto-and-veto rules. Moreover, under mild richness conditions on the domain of preferences over lotteries, any Pareto efficient Nash-implementable rule is a Pareto-and-veto rule and hence is implementable through a strike mechanism.

Suggested Citation

  • Jean-François Laslier & Matías Núñez & M. Remzi Sanver, 2021. "A solution to the two-person implementation problem," Post-Print halshs-03342559, HAL.
    • Handle: RePEc:hal:journl:halshs-03342559
    DOI: 10.1016/j.jet.2021.105261
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    References listed on IDEAS

    as
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    Cited by:

    1. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    2. Anna Bogomolnaia & Ron Holzman & Hervé Moulin, 2021. "Worst Case in Voting and Bargaining," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196999, HAL.
    3. R Jain & V Korpela & M Lombardi, 2022. "Two-Player Rationalizable Implementation," Working Papers 202228, University of Liverpool, Department of Economics.
    4. Bogomolnaia, Anna & Holzman, Ron & Moulin, Hervé, 2023. "On guarantees, vetoes and random dictators," Theoretical Economics, Econometric Society, vol. 18(1), January.
    5. Anna bogomolnaia Ron Holzman Herve Moulin, 2021. "Wost Case in Voting and Bargaining," Papers 2104.02316, arXiv.org.
    6. Mehmet Barlo & Nuh Aygün Dalkıran, 2022. "Computational implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 605-633, December.
    7. Damien Bol & Jean-François Laslier & Matías Núñez, 2022. "Two Person Bargaining Mechanisms: A Laboratory Experiment," Group Decision and Negotiation, Springer, vol. 31(6), pages 1145-1177, December.
    8. Núñez, Matías & Pimienta, Carlos & Xefteris, Dimitrios, 2022. "On the implementation of the median," Journal of Mathematical Economics, Elsevier, vol. 99(C).

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    More about this item

    Keywords

    Nash implementation; Two players; Pareto efficiency;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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