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Multilateral non-cooperative bargaining in a general utility space

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  • Klaus Kultti
  • Hannu Vartiainen

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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  • 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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    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. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
    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. 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).
    6. 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.
    7. 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.
    8. John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 709-724.
    9. Kalyan Chatterjee & Hamid Sabourian, 2000. "Multiperson Bargaining and Strategic Complexity," Econometrica, Econometric Society, vol. 68(6), pages 1491-1510, November.
    10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    11. 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.
    12. Chae Suchan & Yang Jeong-Ae, 1994. "An N-Person Pure Bargaining Game," Journal of Economic Theory, Elsevier, vol. 62(1), pages 86-102, February.
    13. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 61-80.
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    Cited by:

    1. Britz, V. & Herings, P.J.J. & Predtetchinski, A., 2012. "On the convergence to the 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.J.J. & 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, vol. 40(2), pages 263-280, May.
    6. Jenny Simon & Justin Mattias Valasek, 2017. "Centralized Fiscal Spending by Supranational Unions," Economica, London School of Economics and Political Science, vol. 84(333), pages 78-103, January.
    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 336-364, 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, vol. 86(C), 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, vol. 145(5), pages 1951-1967, September.
    11. Anbarci, Nejat & Sun, Ching-jen, 2013. "Asymmetric Nash bargaining solutions: A simple Nash program," Economics Letters, Elsevier, vol. 120(2), pages 211-214.
    12. P. Jean-Jacques Herings & A. Predtetchinski, 2016. "Bargaining under monotonicity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 221-243, June.
    13. 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.
    14. Shunsuke Hanato, 2020. "Equilibrium payoffs and proposal ratios in bargaining models," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 463-494, June.
    15. Kristal K. Trejo & Ruben Juarez & Julio B. Clempner & Alexander S. Poznyak, 2023. "Non-Cooperative Bargaining with Unsophisticated Agents," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 937-974, March.
    16. 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.
    17. Kawamori, Tomohiko & Miyakawa, Toshiji, 2019. "Bargaining delay under partial breakdowns and externalities," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    18. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2021. "Multi-lateral strategic bargaining without stationarity," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    19. 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.

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    More about this item

    Keywords

    Multilateral; Bargaining; General utility set; C7; D7;
    All these keywords.

    JEL classification:

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

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