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Reaching consensus through approval bargaining

Author

Listed:
  • Laslier, Jean-François
  • Núñez, Matías
  • Pimienta, Carlos

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

  • Laslier, Jean-François & Núñez, Matías & Pimienta, Carlos, 2017. "Reaching consensus through approval bargaining," Games and Economic Behavior, Elsevier, vol. 104(C), pages 241-251.
  • Handle: RePEc:eee:gamebe:v:104:y:2017:i:c:p:241-251
    DOI: 10.1016/j.geb.2017.04.002
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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. Danila Serra, 2008. "Bargaining for bribes under uncertainty," CSAE Working Paper Series 2008-22, Centre for the Study of African Economies, University of Oxford.
    3. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    4. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    5. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    6. Matsushima, Hitoshi, 2008. "Role of honesty in full implementation," Journal of Economic Theory, Elsevier, vol. 139(1), pages 353-359, March.
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    9. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    10. Matsushima, Hitoshi, 2008. "Behavioral aspects of implementation theory," Economics Letters, Elsevier, vol. 100(1), pages 161-164, July.
    11. Francesca Busetto & Giulio Codognato, 2009. "Reconsidering two-agent Nash implementation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 171-179, February.
    12. 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.
    13. Ortner, Juan, 2015. "Direct implementation with minimally honest individuals," Games and Economic Behavior, Elsevier, vol. 90(C), pages 1-16.
    14. 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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    18. Danila Serra, 2008. "Bargaining for bribes under uncertainty," Economics Series Working Papers CSAE WPS/2008-22, University of Oxford, Department of Economics.
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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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