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Stationary perfect equilibria of an n-person noncooperative bargaining game and cooperative solution concepts

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  • Kim, Taekwon
  • Jeon, Yongil

Abstract

This paper characterizes the stationary (subgame) perfect equilibria of an n-person noncooperative bargaining model with characteristic functions, and provides strategic foundations of some cooperative solution concepts such as the core, the bargaining set and the kernel. The contribution of this paper is twofold. First, we show that a linear programming formulation successfully characterizes the stationary (subgame) perfect equilibria of our bargaining game. We suggest a linear programming formulation as an algorithm for the stationary (subgame) perfect equilibria of a class of n-person noncooperative games. Second, utilizing the linear programming formulation, we show that stationary (subgame) perfect equilibria of n-person noncooperative games provide strategic foundations for the bargaining set and the kernel.

Suggested Citation

  • Kim, Taekwon & Jeon, Yongil, 2009. "Stationary perfect equilibria of an n-person noncooperative bargaining game and cooperative solution concepts," European Journal of Operational Research, Elsevier, vol. 194(3), pages 922-932, May.
    • Handle: RePEc:eee:ejores:v:194:y:2009:i:3:p:922-932
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    5. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-1364, November.
    6. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    7. Roth,Alvin E. (ed.), 1986. "Game-Theoretic Models of Bargaining," Cambridge Books, Cambridge University Press, number 9780521267571, October.
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    Cited by:

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    2. Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2013. "Subgame-perfection in free transition games," European Journal of Operational Research, Elsevier, vol. 228(1), pages 201-207.
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    4. Zheng-Hai Huang & Liqun Qi, 2017. "Formulating an n-person noncooperative game as a tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 66(3), pages 557-576, April.
    5. Marco Rogna, 2022. "The Burning Coalition Bargaining Model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 735-768, October.
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    7. Rogna, Marco, 2021. "The central core and the mid-central core as novel set-valued and point-valued solution concepts for transferable utility coalitional games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 1-11.
    8. Wu, Qiong & Ren, Hongbo & Gao, Weijun & Ren, Jianxing & Lao, Changshi, 2017. "Profit allocation analysis among the distributed energy network participants based on Game-theory," Energy, Elsevier, vol. 118(C), pages 783-794.

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