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Sequential Share Bargaining

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  • Herings, P. Jean-Jacques
  • Predtetchinski, Arkadi

    (METEOR)

Abstract

This paper presents a new extension of the Rubinstein-St°ahl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players’ shares in the cake are determined sequentially. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. In equilibrium, agreement is reached immediately. The results are therefore qualitatively the same as in the two player case. The result builds on an analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor, and that also in one-dimensional bargaining problems agreement is reached immediately.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 005.

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Date of creation: 2007
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Handle: RePEc:unm:umamet:2007005

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Keywords: microeconomics ;

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References

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  1. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  2. Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, Elsevier, vol. 84(3), pages 407-411, September.
  3. Chen-Ying Huang, 2002. "Multilateral bargaining: conditional and unconditional offers," Economic Theory, Springer, Springer, vol. 20(2), pages 401-412.
  4. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2007. "One-dimensional Bargaining with Markov Recognition Probabilities," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 044, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Haller, Hans, 1986. "Non-cooperative bargaining of N [ges] 3 players," Economics Letters, Elsevier, Elsevier, vol. 22(1), pages 11-13.
  6. 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.
  7. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  8. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 63(2), pages 371-99, March.
  9. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 1047-64, July.
  10. Seok-ju Cho & John Duggan, 2001. "Uniqueness of Stationary Equilibria in a one-Dimensional Model of Bargaining," Wallis Working Papers, University of Rochester - Wallis Institute of Political Economy WP23, University of Rochester - Wallis Institute of Political Economy.
  11. Imai, Haruo & Salonen, Hannu, 2000. "The representative Nash solution for two-sided bargaining problems," Mathematical Social Sciences, Elsevier, Elsevier, vol. 39(3), pages 349-365, May.
  12. Yang, Jeong-Ae, 1992. "Another n-person bargaining game with a unique perfect equilibrium," Economics Letters, Elsevier, Elsevier, vol. 38(3), pages 275-277, March.
  13. Chae, Suchan & Yang, Jeong-Ae, 1988. "The unique perfect equilibrium of an n-person bargaining game," Economics Letters, Elsevier, Elsevier, vol. 28(3), pages 221-223.
  14. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, Elsevier, vol. 137(1), pages 627-651, November.
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Cited by:
  1. Hurt, Wesley & Osório, António (António Miguel), 2014. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," Working Papers, Universitat Rovira i Virgili, Department of Economics 2072/237596, Universitat Rovira i Virgili, Department of Economics.
  2. Erik Ansink & Hans-Peter Weikard, 2009. "Sequential Sharing Rules for River Sharing Problems," Working Papers, Fondazione Eni Enrico Mattei 2009.114, Fondazione Eni Enrico Mattei.
  3. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(1), pages 189-215, January.
  4. Hurt, Wesley & Osorio, Antonio, 2014. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," MPRA Paper 56690, University Library of Munich, Germany.

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