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Multilateral non-cooperative bargaining in a general utility space

Author

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  • Klaus Kultti

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  • Hannu Vartiainen

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Abstract

We consider an n-player bargaining problem where the utility possibility set is compact, convex, and stricly comprehensive. We show that a stationary subgame perfect Nash equilibrium exists, and that, if the Pareto surface is differentiable, all such equilibria converge to the Nash bargaining solution as the length of a time period between offers goes to zero. Without the differentiability assumption, convergence need not hold.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:39:y:2010:i:4:p:677-689 DOI: 10.1007/s00182-009-0212-3
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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, pages 97-109.
    2. 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.
    3. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, December.
    4. Chae, Suchan & Yang, Jeong-Ae, 1988. "The unique perfect equilibrium of an n-person bargaining game," Economics Letters, Elsevier, vol. 28(3), pages 221-223.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Suh, Sang-Chul & Wen, Quan, 2006. "Multi-agent bilateral bargaining and the Nash bargaining solution," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 61-73, February.
    7. Kalyan Chatterjee & Hamid Sabourian, 2000. "Multiperson Bargaining and Strategic Complexity," Econometrica, Econometric Society, vol. 68(6), pages 1491-1510, November.
    8. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
    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).
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    Citations

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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. Britz V. & Herings P.J.J. & Predtetchinski A., 2014. "Equilibrium delay and non-existence of equilibrium in unanimity bargaining games," Research Memorandum 019, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. 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).
    4. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2011. "On the asymptotic uniqueness of bargaining equilibria," Economics Letters, Elsevier, vol. 111(3), pages 243-246, June.
    5. Francis Bloch & Effrosyni Diamantoudi, 2011. "Noncooperative formation of coalitions in hedonic games," International Journal of Game Theory, Springer;Game Theory Society, pages 263-280.
    6. Anbarci, Nejat & Sun, Ching-jen, 2013. "Asymmetric Nash bargaining solutions: A simple Nash program," Economics Letters, Elsevier, pages 211-214.
    7. Thorsten Upmann & Julia Müller, 2014. "The Structure of Firm-Specific Labour Unions," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 170(2), pages 336-385, June.
    8. 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, pages 178-183.
    9. Kawamori, Tomohiko, 2014. "A noncooperative foundation of the asymmetric Nash bargaining solution," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 12-15.
    10. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, pages 1951-1967.
    11. P. Jean-Jacques Herings & A. Predtetchinski, 2016. "Bargaining under monotonicity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 221-243.
    12. 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.
    13. 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.
    14. Christian Siegel & Zsofia Barany, 2017. "Disentangling Occupation- and Sector-specific Technological Change," 2017 Meeting Papers 997, Society for Economic Dynamics.
    15. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0567-9 is not listed on IDEAS

    More about this item

    Keywords

    Multilateral; Bargaining; General utility set; C7; D7;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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