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On the Asymptotic Uniqueness of Bargaining Equilibria

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  • Herings P. Jean-Jacques
  • Predtetchinski Arkadi

    (METEOR)

Abstract

This note reexamines the connection between the asymmetric Nash bargaining solution and the equilibria of strategic bargaining games. Several papers in the literature obtain the asymmetric Nash bargaining solution as the unique limit of subgame perfect equilibria in stationary strategies when the breakdown probability approaches zero. This note illustrates by means of two examples that this result depends crucially on the differentiability of the boundary of the set of feasible payoffs. In the first example the game has a unique stationary subgame perfect equilibrium that fails to converge to the asymmetric Nash bargaining solution. In the second example the game has two stationary subgame perfect equilibria that converge to two distinct limits as the breakdown probability vanishes. This example demonstrates that without differentiability of the set of feasible payoffs there is not even asymptotic uniqueness of stationary equilibria in the bargaining model.

Suggested Citation

  • Herings P. Jean-Jacques & Predtetchinski Arkadi, 2010. "On the Asymptotic Uniqueness of Bargaining Equilibria," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2010010
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    3. Predtetchinski, Arkadi, 2011. "One-dimensional bargaining," Games and Economic Behavior, Elsevier, vol. 72(2), pages 526-543, June.
    4. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-399, March.
    5. Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 309-329, June.
    6. Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
    7. Klaus Kultti & Hannu Vartiainen, 2010. "Multilateral non-cooperative bargaining in a general utility space," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 677-689, October.
    8. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1951-1967, September.
    9. Kultti, Klaus & Vartiainen, Hannu, 2007. "Von Neumann-Morgenstern stable sets, discounting, and Nash bargaining," Journal of Economic Theory, Elsevier, vol. 137(1), pages 721-728, November.
    10. Lensberg, T. & Thomson, W., 1988. "Characterizing The Nash Bargaining Solution Without Pareto-Optimality," RCER Working Papers 136, University of Rochester - Center for Economic Research (RCER).
    11. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    12. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    13. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
    14. Predtetchinski, Arkadi, 2007. "One-dimensional bargaining with a general voting rule," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    16. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(01), pages 73-88, March.
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    Cited by:

    1. Herings P. Jean-Jacques & Britz Volker & Predtetchinski Arkadi, 2012. "On the Convergence to Nash Bargaining Solution for Endogenous Bargaining Protocols," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Herings P. Jean-Jacques & Predtetchinski A., 2011. "Procedurally Fair Income Taxation Schemes," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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