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Multi-Agent Bilateral Bargaining and the Nash Bargaining Solution

Author

Listed:
  • Sang-Chul Suh

    (Department of Economics, University of Windsor)

  • Quan Wen

    (Department of Economics, Vanderbilt University)

Abstract
This paper studies a bargaining model where n players play a sequence of (n-1) bilateral bargaining sessions. In each bilateral bargaining session, two players follow the same bargaining process as in Rubinstein's (1982). A partial agreement between two players is reached in the session and one player effectively leaves the game with a share agreed upon in the partial agreement and the other moves on to the next session. Such a (multi-agent) bilateral bargaining model admits a unique subgame perfect equilibrium. Depending on who exits and who stays, we consider two bargaining procedures. The equilibrium outcomes under the two bargaining procedures converge to the Nash (1950) bargaining solution of the corresponding bargaining problem as the players' discount factor goes to one. Thus, the bilateral bargaining model studied in this paper provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.

Suggested Citation

  • Sang-Chul Suh & Quan Wen, 2003. "Multi-Agent Bilateral Bargaining and the Nash Bargaining Solution," Vanderbilt University Department of Economics Working Papers 0306, Vanderbilt University Department of Economics.
    • Handle: RePEc:van:wpaper:0306
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    References listed on IDEAS

    as
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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. Mariotti, Marco & Wen, Quan, 2021. "A noncooperative foundation of the competitive divisions for bads," Journal of Economic Theory, Elsevier, vol. 194(C).
    3. Yulan Wang & Baozhuang Niu & Pengfei Guo & Jing-Sheng Song, 2021. "Direct Sourcing or Agent Sourcing? Contract Negotiation in Procurement Outsourcing," Manufacturing & Service Operations Management, INFORMS, vol. 23(2), pages 294-310, March.
    4. Izat B. Baybusinov & Enrico Maria Fenoaltea & Yi-Cheng Zhang, 2022. "Negotiation problem," Papers 2201.12619, arXiv.org.
    5. Baybusinov, Izat B. & Fenoaltea, Enrico Maria & Zhang, Yi-Cheng, 2022. "Negotiation problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    6. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "A sequential bargaining protocol for land rental arrangements," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 65-99, June.
    7. Acuna, Jorge A. & Zayas-Castro, Jose L. & Feijoo, Felipe, 2022. "A bilevel Nash-in-Nash model for hospital mergers: A key to affordable care," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    8. Alejandro Caparrós, 2016. "Bargaining and International Environmental Agreements," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 5-31, September.
    9. P. Herings & Arkadi Predtetchinski, 2012. "Sequential share bargaining," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 301-323, May.
    10. Sang-Chul Suh & Quan Wen, 2003. "Multi-Agent Bilateral Bargaining with Endogenous Protocol," Vanderbilt University Department of Economics Working Papers 0305, Vanderbilt University Department of Economics.
    11. Fabien Tripier, 2014. "A Search-Theoretic Approach to Efficient Financial Intermediation," Working Papers 2014-18, CEPII research center.
    12. 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.
    13. 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.
    14. Bedayo, Mikel & Mauleon, Ana & Vannetelbosch, Vincent, 2016. "Bargaining in endogenous trading networks," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 70-82.
    15. Soumendu Sarkar & Dhritiman Gupta, 2023. "Bargaining for assembly," Theory and Decision, Springer, vol. 95(2), pages 229-254, August.
    16. Edwin L.-C. Lai, 2008. "The most-favored nation rule in club enlargement negotiation," Working Papers 0815, Federal Reserve Bank of Dallas.
    17. Vidal-Puga, Juan J., 2008. "Forming coalitions and the Shapley NTU value," European Journal of Operational Research, Elsevier, vol. 190(3), pages 659-671, November.
    18. Yi-Chun Chen & Xiao Luo, 2008. "Delay in a bargaining game with contracts," Theory and Decision, Springer, vol. 65(4), pages 339-353, December.
    19. Sang-Chul Suh & Quan Wen, 2009. "A multi-agent bilateral bargaining model with endogenous protocol," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 203-226, August.
    20. Qi Feng & Chengzhang Li & Mengshi Lu & J. George Shanthikumar, 2022. "Implementing Environmental and Social Responsibility Programs in Supply Networks Through Multiunit Bilateral Negotiation," Management Science, INFORMS, vol. 68(4), pages 2579-2599, April.
    21. Dijkstra, Bouwe R. & Nentjes, Andries, 2020. "Pareto-Efficient Solutions for Shared Public Good Provision: Nash Bargaining versus Exchange-Matching-Lindahl," Resource and Energy Economics, Elsevier, vol. 61(C).
    22. 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; subgame perfect equilibrium; Nash bargaining solution;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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