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Competitive outcomes and the core of TU market games

Author

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  • Brangewitz, Sonja

    (Center for Mathematical Economics, Bielefeld University)

  • Gamp, Jan-Philip

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We investigate the relationship between certain subsets of the core for TU market games and competitive payoff vectors of certain markets linked to that game. This can be considered as the case in between the two extreme cases of Shapley and Shubik (1975). They remark already that their result can be extended to any closed convex subset of the core, but they omit the details of the proof which we present here. This more general case is in particular interesting, as the two theorems of Shapley and Shubik (1975) are included as special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:bie:wpaper:454
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    File URL: https://pub.uni-bielefeld.de/download/2671702/2671703
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    References listed on IDEAS

    as
    1. 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.
    2. Qin, Cheng-Zhong, 1993. "A Conjecture of Shapley and Shubik on Competitive Outcomes in the Cores of NTU Market Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(4), pages 335-344.
    3. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    4. Brangewitz, Sonja & Gamp, Jan-Philip, 2016. "Competitive outcomes and the inner core of NTU market games," Center for Mathematical Economics Working Papers 449, Center for Mathematical Economics, Bielefeld University.
    5. Garratt, Rod & Qin, Cheng-Zhong, 2000. "On Market Games When Agents Cannot Be in Two Places at Once," Games and Economic Behavior, Elsevier, vol. 31(2), pages 165-173, May.
    6. 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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    Cited by:

    1. 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.
    2. 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.

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