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Multi-Agent Bilateral Bargaining and the Nash Bargaining Solution

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  • Sang-Chul Suh

    ()
    (Department of Economics, University of Windsor)

  • Quan Wen

    ()
    (Department of Economics, Vanderbilt University)

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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.

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File URL: http://www.accessecon.com/pubs/VUECON/vu03-w06.pdf
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0306.

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Date of creation: Mar 2003
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Handle: RePEc:van:wpaper:0306

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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Keywords: Multilateral bargaining; subgame perfect equilibrium; Nash bargaining solution;

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References

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  1. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  2. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, October.
  3. Kalyan Chatterjee & Hamid Sabourian, 1998. "Multiperson Bargaining and Strategic Complexity," CRIEFF Discussion Papers 9808, Centre for Research into Industry, Enterprise, Finance and the Firm.
  4. Chen-Ying Huang, 2002. "Multilateral bargaining: conditional and unconditional offers," Economic Theory, Springer, vol. 20(2), pages 401-412.
  5. Asheim, Geir B., 1992. "A unique solution to n-person sequential bargaining," Games and Economic Behavior, Elsevier, vol. 4(2), pages 169-181, April.
  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  7. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  8. Thomson, W., 1998. "Consistency and its Converse: an Introduction," RCER Working Papers 448, University of Rochester - Center for Economic Research (RCER).
  9. repec:cup:cbooks:9780521343831 is not listed on IDEAS
  10. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  11. 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.
  12. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  13. Houba, Harold, 1993. "An alternative proof of uniqueness in non-cooperative bargaining," Economics Letters, Elsevier, vol. 41(3), pages 253-256.
  14. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-64, November.
  15. Yang, Jeong-Ae, 1992. "Another n-person bargaining game with a unique perfect equilibrium," Economics Letters, Elsevier, vol. 38(3), pages 275-277, March.
  16. Cai, Hongbin, 2000. "Delay in Multilateral Bargaining under Complete Information," Journal of Economic Theory, Elsevier, vol. 93(2), pages 260-276, August.
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Citations

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Cited by:
  1. Hannu Vartiainen & Klaus Kultti, 2007. "Multilateral Non-Cooperative Bargaining in a General Utility Space," Discussion Papers 19, Aboa Centre for Economics.
  2. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2007. "Sequential Share Bargaining," Research Memorandum 005, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Sang-Chul Suh & Quan Wen, 2009. "A multi-agent bilateral bargaining model with endogenous protocol," Economic Theory, Springer, vol. 40(2), pages 203-226, August.
  4. Yi-Chun Chen & Xiao Luo, 2008. "Delay in a bargaining game with contracts," Theory and Decision, Springer, vol. 65(4), pages 339-353, December.
  5. Edwin L.-C. Lai, 2008. "The most-favored nation rule in club enlargement negotiation," Working Papers 0815, Federal Reserve Bank of Dallas.
  6. 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).
  7. BRITZ, Volker & HERINGS, Jean-Jacques & PREDTETCHINSKI, Arkadi, 2013. "On the Convergence to the Nash bargaining solution for action-dependent bargaining protocols," CORE Discussion Papers 2013044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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