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A solution to the two-person implementation problem

Author

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  • Jean-François Laslier

    (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - 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 Paris - 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)

  • Matias Nunez

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Economie et Statistique [Bruz] - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz])

  • 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 twoperson 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 unvetoed 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 & Matias Nunez & M Remzi Sanver, 2020. "A solution to the two-person implementation problem," PSE Working Papers halshs-02173504, HAL.
  • Handle: RePEc:hal:psewpa:halshs-02173504
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/halshs-02173504v3
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    References listed on IDEAS

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    Cited by:

    1. Anna Bogomolnaia & Ron Holzman & Hervé Moulin, 2021. "Worst Case in Voting and Bargaining," Post-Print halshs-03196999, HAL.
    2. Anna bogomolnaia Ron Holzman Herve Moulin, 2021. "Wost Case in Voting and Bargaining," Papers 2104.02316, arXiv.org.

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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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