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Competitive outcomes and endogenous coalition formation in an n-person game

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  • Sun, Ning
  • Trockel, Walter
  • Yang, Zaifu

Abstract

We extend the analysis of competitive outcomes in TU market games of Shapley and Shubik [Shapley, L.S., Shubik, M., 1975. Competitive outcomes in the cores of market games. International Journal of Game Theory 4, 229-237] in two ways. First, our representing economies are coalition production economies. Second, and more importantly, our analysis holds for arbitrary TU games. By adopting the C-stable set of Guesnerie and Oddou [Guesnerie, R., Oddou, C., 1979. On economic games which are not necessarily superadditive. Economics Letters 3, 301-306], renamed c-core in our paper, we are able to characterize competitive outcomes even in games with empty core. As competitive outcomes are associated with specific coalition structures, our main result provides an endogenous determination of coalition building and shows that the c-core of any TU game coincides with the set of competitive outcomes of the corresponding coalition production economy.

Suggested Citation

  • Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:7-8:p:853-860
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    Cited by:

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    2. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    3. Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2021. "Cohesive efficiency in TU-games: axiomatizations of variants of the Shapley value, egalitarian values and their convex combinations," Annals of Operations Research, Springer, vol. 302(1), pages 23-47, July.
    4. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
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    6. Camelia Bejan & Juan Camilo Gómez, 2017. "Employment lotteries, endogenous firm formation and the aspiration core," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 215-226, October.
    7. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    8. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Efficiency and Duality," Working Papers CIE 138, Paderborn University, CIE Center for International Economics.
    9. Aslan, Fatma & Duman, Papatya & Trockel, Walter, 2019. "Duality for General TU-games Redefined," Center for Mathematical Economics Working Papers 620, Center for Mathematical Economics, Bielefeld University.
    10. Brangewitz, Sonja & Gamp, Jan-Philip, 2016. "Inner Core, Asymmetric Nash Bargaining Solutions and Competitive Payoffs," Center for Mathematical Economics Working Papers 453, Center for Mathematical Economics, Bielefeld University.
    11. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Duality and P-core," Working Papers CIE 136, Paderborn University, CIE Center for International Economics.
    12. Hirbod Assa & Sheridon Elliston & Ehud Lehrer, 2016. "Joint games and compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 91-113, January.
    13. Sonja Brangewitz & Jan-Philip Gamp, 2014. "Competitive outcomes and the inner core of NTU market games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 529-554, November.
    14. Zhao, Jingang, 2008. "The Maximal Payoff and Coalition Formation in Coalitional Games," Coalition Theory Network Working Papers 6298, Fondazione Eni Enrico Mattei (FEEM).
    15. Brangewitz, Sonja & Gamp, Jan-Philip, 2014. "Competitive outcomes and the core of TU market games," Center for Mathematical Economics Working Papers 454, Center for Mathematical Economics, Bielefeld University.
    16. Inoue, Tomoki, 2012. "Representation of transferable utility games by coalition production economies," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 143-147.
    17. Inoue, Tomoki, 2013. "Representation of non-transferable utility games by coalition production economies," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 141-149.
    18. Jingang Zhao, 2018. "A Reexamination of the Coase Theorem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 3(1), pages 111-132, December.
    19. Ju, Yuan, 2012. "Reject and renegotiate: The Shapley value in multilateral bargaining," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 431-436.
    20. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    21. Bejan, Camelia & Gómez, Juan Camilo, 2012. "A market interpretation of the proportional extended core," Economics Letters, Elsevier, vol. 117(3), pages 636-638.
    22. Inoue, Tomoki, 2011. "Representation of TU games by coalition production economies," Center for Mathematical Economics Working Papers 430, Center for Mathematical Economics, Bielefeld University.

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    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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