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Sequential Share Bargaining

Author

Listed:
  • 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.

Suggested Citation

  • 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).
  • Handle: RePEc:unm:umamet:2007005
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    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    3. Imai, Haruo & Salonen, Hannu, 2000. "The representative Nash solution for two-sided bargaining problems," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 349-365, May.
    4. Haller, Hans, 1986. "Non-cooperative bargaining of N [ges] 3 players," Economics Letters, Elsevier, vol. 22(1), pages 11-13.
    5. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-399, March.
    6. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    7. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
    8. 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.
    9. Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
    10. 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.
    11. 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.
    12. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(01), pages 73-88, March.
    13. Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
    14. Yang, Jeong-Ae, 1992. "Another n-person bargaining game with a unique perfect equilibrium," Economics Letters, Elsevier, vol. 38(3), pages 275-277, March.
    15. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
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    Citations

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    Cited by:

    1. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    2. Osório, António (António Miguel), 2017. "Self-interest and Equity Concerns: A Behavioural Allocation Rule for Operational Problems," Working Papers 2072/290757, Universitat Rovira i Virgili, Department of Economics.
    3. Daniel Cardona & Antoni Rubí-Barceló, 2016. "Time-Preference Heterogeneity and Multiplicity of Equilibria in Two-Group Bargaining," Games, MDPI, Open Access Journal, vol. 7(2), pages 1-17, May.
    4. repec:gam:jgames:v:7:y:2016:i:2:p:12:d:69916 is not listed on IDEAS
    5. Hurt, Wesley & Osório, António (António Miguel), 2014. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," Working Papers 2072/237596, Universitat Rovira i Virgili, Department of Economics.
    6. Osório, António, 2017. "Self-interest and equity concerns: A behavioural allocation rule for operational problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 205-213.
    7. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    8. Osorio, Antonio, 2014. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," MPRA Paper 56690, University Library of Munich, Germany.
    9. Herings P.J.J. & Houba H, 2015. "Costless delay in negotiations," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
    10. Osório, António (António Miguel), 2016. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," Working Papers 2072/266574, Universitat Rovira i Virgili, Department of Economics.

    More about this item

    Keywords

    microeconomics ;

    JEL classification:

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

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