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Multi-agent bilateral bargaining and the Nash bargaining solution

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  • Suh, Sang-Chul
  • Wen, Quan
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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 42 (2006)
Issue (Month): 1 (February)
Pages: 61-73

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Handle: RePEc:eee:mateco:v:42:y:2006:i:1:p:61-73

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Web page: http://www.elsevier.com/locate/jmateco

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  1. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, November.
  2. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
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  4. Thomson,William & Lensberg,Terje, 1989. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521343831, December.
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  8. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  9. Chatterjee, K. & Sabourian, H., 1997. "Multiperson Bargaining and Strategic Complexity," Cambridge Working Papers in Economics 9733, Faculty of Economics, University of Cambridge.
  10. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  11. Chen-Ying Huang, 2002. "Multilateral bargaining: conditional and unconditional offers," Economic Theory, Springer, vol. 20(2), pages 401-412.
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  14. Asheim, Geir B., 1992. "A unique solution to n-person sequential bargaining," Games and Economic Behavior, Elsevier, vol. 4(2), pages 169-181, April.
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Cited by:
  1. Klaus Kultti & Hannu Vartiainen, 2010. "Multilateral non-cooperative bargaining in a general utility space," International Journal of Game Theory, Springer, vol. 39(4), pages 677-689, October.
  2. 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.
  3. P. Herings & Arkadi Predtetchinski, 2012. "Sequential share bargaining," International Journal of Game Theory, Springer, vol. 41(2), pages 301-323, May.
  4. 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).
  5. 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).
  6. Yi-Chun Chen & Xiao Luo, 2008. "Delay in a bargaining game with contracts," Theory and Decision, Springer, vol. 65(4), pages 339-353, December.
  7. Edwin L.-C. Lai, 2008. "The most-favored nation rule in club enlargement negotiation," Working Papers 0815, Federal Reserve Bank of Dallas.
  8. 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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