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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 - IP Paris - Institut Polytechnique de Paris - 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 Herve Moulin, 2021. "Wost Case in Voting and Bargaining," Papers 2104.02316, arXiv.org.
    3. Ritesh Jain & Ville Korpela & Michele Lombardi, 2022. "Two-Player Rationalizable Implementation," CSEF Working Papers 660, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. 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.
    5. Núñez, Matías & Pimienta, Carlos & Xefteris, Dimitrios, 2022. "On the implementation of the median," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. 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.
    7. Bogomolnaia, Anna & Holzman, Ron & Moulin, Hervé, 2023. "On guarantees, vetoes and random dictators," Theoretical Economics, Econometric Society, vol. 18(1), January.
    8. Mehmet Barlo & Nuh Aygün Dalkıran, 2022. "Computational implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 605-633, December.

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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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