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Reaching consensus through approval bargaining

Author

Listed:
  • Jean-François Laslier

    (PSE - Paris School of Economics, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

  • Matias Nunez

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

  • Carlos Pimienta

    (UNSW - University of New South Wales [Sydney])

Abstract

In the Approval Bargaining game, two players bargain over a finite set of alternatives. To this end, each one simultaneously submits a utility function u jointly with a real number α; by doing so she approves the lotteries whose expected utility according to u is at least α. The lottery to be implemented is randomly selected among the most approved ones. We first prove that there is an equilibrium where players truthfully reveal their utility function. We also show that, in any equilibrium, the equilibrium outcome is approved by both players. Finally, every equilibrium is sincere and Pareto efficient as long as both players are partially honest.

Suggested Citation

  • Jean-François Laslier & Matias Nunez & Carlos Pimienta, 2017. "Reaching consensus through approval bargaining," Post-Print halshs-01630037, HAL.
  • Handle: RePEc:hal:journl:halshs-01630037
    DOI: 10.1016/j.geb.2017.04.002
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01630037
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    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    5. Matsushima, Hitoshi, 2008. "Role of honesty in full implementation," Journal of Economic Theory, Elsevier, vol. 139(1), pages 353-359, March.
    6. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
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    8. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
    9. Matias Nunez & Jean-François Laslier, 2015. "Bargaining through Approval," Working Papers halshs-01168675, HAL.
    10. Kartik, Navin & Tercieux, Olivier, 2012. "Implementation with evidence," Theoretical Economics, Econometric Society, vol. 7(2), May.
    11. Matsushima, Hitoshi, 2008. "Behavioral aspects of implementation theory," Economics Letters, Elsevier, vol. 100(1), pages 161-164, July.
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    15. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
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    More about this item

    Keywords

    Approval voting; Bargaining; Partial honesty; Consensual equilibrium;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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