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Multi-Agent Bilateral Bargaining and the Nash Bargaining Solution

  • Sang-Chul Suh


    (Department of Economics, University of Windsor)

  • Quan Wen


    (Department of Economics, Vanderbilt University)

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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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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  1. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  2. Chatterjee, K. & Sabourian, H., 1997. "Multiperson Bargaining and Strategic Complexity," Cambridge Working Papers in Economics 9733, Faculty of Economics, University of Cambridge.
  3. Quan Wen & Sang-Chul Suh, 2004. "Multi-Agent Bilateral Bargaining with Endogenous Protocol," Econometric Society 2004 Far Eastern Meetings 405, Econometric Society.
  4. Asheim, G.B., 1989. "A Unique Solution To N-Person Sequential Bargaining," Papers 11-89, Norwegian School of Economics and Business Administration-.
  5. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  6. Yang, Jeong-Ae, 1992. "Another n-person bargaining game with a unique perfect equilibrium," Economics Letters, Elsevier, vol. 38(3), pages 275-277, March.
  7. 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.
  8. Thomson,William & Lensberg,Terje, 1989. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521343831, April.
  9. John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 709-724.
  10. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, 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. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  13. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
  14. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, April.
  15. Cai, Hongbin, 2000. "Delay in Multilateral Bargaining under Complete Information," Journal of Economic Theory, Elsevier, vol. 93(2), pages 260-276, August.
  16. Houba, H., 1993. "An alternative proof of uniqueness in non-cooperative bargaining," Serie Research Memoranda 0015, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  17. Chen-Ying Huang, 2002. "Multilateral bargaining: conditional and unconditional offers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 401-412.
  18. Haller, Hans, 1986. "Non-cooperative bargaining of N [ges] 3 players," Economics Letters, Elsevier, vol. 22(1), pages 11-13.
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