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On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

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  • BRITZ, Volker
  • HERINGS, P. Jean-Jacques
  • PREDTETCHINSKI, Arkadi

Abstract

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.
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Suggested Citation

  • BRITZ, Volker & HERINGS, P. Jean-Jacques & PREDTETCHINSKI, Arkadi, 2014. "On the convergence to the Nash bargaining solution for action-dependent bargaining protocols," LIDAM Reprints CORE 2622, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2622
    Note: In : Games and Economic Behavior, 86, 178-183, 2014
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    Citations

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    Cited by:

    1. Britz, Volker, 2018. "Rent-seeking and surplus destruction in unanimity bargaining," Games and Economic Behavior, Elsevier, vol. 109(C), pages 1-20.
    2. Ching-jen Sun, 2018. "The bargaining correspondence: when Edgeworth meets Nash," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 337-359, August.
    3. Mariotti, Marco & Wen, Quan, 2021. "A noncooperative foundation of the competitive divisions for bads," Journal of Economic Theory, Elsevier, vol. 194(C).
    4. Volker Britz & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2014. "Equilibrium Delay and Non-existence of Equilibrium in Unanimity Bargaining Games," CER-ETH Economics working paper series 14/196, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    5. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2015. "Delay, multiplicity, and non-existence of equilibrium in unanimity bargaining games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 192-202.
    6. Gersbach, Hans & Britz, Volker, 2018. "Open Rule Legislative Bargaining," CEPR Discussion Papers 12966, C.E.P.R. Discussion Papers.
    7. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2014. "On the convergence to the Nash bargaining solution for action-dependent bargaining protocols," Games and Economic Behavior, Elsevier, vol. 86(C), pages 178-183.
    8. François Maniquet & Massimo Morelli, 2015. "Approval quorums dominate participation quorums," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 1-27, June.
    9. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    10. Volker Britz, 2016. "Destroying Surplus and Buying Time in Unanimity Bargaining," CER-ETH Economics working paper series 16/248, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    11. YATSENKO, Yuri & HRITONENKO, Natali & BRECHET, Thierry, 2014. "Modeling of environmental adaptation versus pollution mitigation," LIDAM Discussion Papers CORE 2014006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. DASH, Sanjeeb & GÜNLÜK, Oktay & WOLSEY, Laurence A., 2014. "The continuous knapsack set," LIDAM Discussion Papers CORE 2014007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2021. "Multi-lateral strategic bargaining without stationarity," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    14. Chaturvedi, Rakesh, 2016. "Efficient coalitional bargaining with noncontingent offers," Games and Economic Behavior, Elsevier, vol. 100(C), pages 125-141.
    15. Bram Driesen & Peter Eccles & Nora Wegner, 2017. "A non-cooperative foundation for the continuous Raiffa solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1115-1135, November.
    16. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.

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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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