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A non-cooperative interpretation of the kernel

Author

Listed:
  • Chih Chang

    (National Tsing Hua University)

  • Cheng-Cheng Hu

    (National Cheng Kung University)

Abstract

The purpose of the paper is to propose a bargaining game to interpret the kernel non-cooperatively. Based on the idea of the Davis-Maschler reduced game, a bilateral bargaining procedure is provided in our game model. We show that the set of all subgame perfect equilibrium outcomes of our non-cooperative game coincides with the kernel for transferable utility games.

Suggested Citation

  • Chih Chang & Cheng-Cheng Hu, 2017. "A non-cooperative interpretation of the kernel," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 185-204, March.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-016-0529-7
    DOI: 10.1007/s00182-016-0529-7
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    References listed on IDEAS

    as
    1. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Potters, Jos & Sudholter, Peter, 1999. "Airport problems and consistent allocation rules," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 83-102, July.
    4. Serrano, Roberto & Vohra, Rajiv, 2002. "Bargaining and Bargaining Sets," Games and Economic Behavior, Elsevier, vol. 39(2), pages 292-308, May.
    5. Hu, Cheng-Cheng, 2007. "A noncooperative interpretation of the Aumann-Davis-Maschler bargaining set," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 203-217, December.
    6. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    7. Chang, Chih & Hu, Cheng-Cheng, 2008. "A non-cooperative interpretation of the f-just rules of bankruptcy problems," Games and Economic Behavior, Elsevier, vol. 63(1), pages 133-144, May.
    8. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    2. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    3. Juan D. Moreno‐Ternero & Min‐Hung Tsay & Chun‐Hsien Yeh, 2022. "Strategic justifications of the TAL family of rules for bankruptcy problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 92-102, March.
    4. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    5. Yang, Guangjing & Sun, Hao & Hou, Dongshuang & Xu, Genjiu, 2020. "A noncooperative bargaining game with endogenous protocol and partial breakdown," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 34-40.

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    More about this item

    Keywords

    Bargaining game; Kernel; Nash program; Subgame perfect equilibrium;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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