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On Bargaining Sets of Convex NTU Games

Author

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  • Bezalel Peleg
  • Peter Sudholter

Abstract

We show that the Aumann-Davis-Maschler bargaining set and the Mas-Colell bargaining set of a non-leveled NTU game that is either ordinal convex or coalition merge convex coincides with the core of the game. Moreover, we show by means of an example that the foregoing statement may not be valid if the NTU game is marginal convex.

Suggested Citation

  • Bezalel Peleg & Peter Sudholter, 2015. "On Bargaining Sets of Convex NTU Games," Discussion Paper Series dp681, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp681
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    References listed on IDEAS

    as
    1. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
    2. Ron Holzman & Bezalel Peleg & Peter Sudhölter, 2007. "Bargaining Sets of Majority Voting Games," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 857-872, November.
    3. Csóka, Péter & Jean-Jacques Herings, P. & Kóczy, László Á. & Pintér, Miklós, 2011. "Convex and exact games with non-transferable utility," European Journal of Operational Research, Elsevier, vol. 209(1), pages 57-62, February.
    4. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    5. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
    6. Ron Holzman, 2001. "The comparability of the classical and the Mas-Colell bargaining sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 543-553.
    7. Peleg, Bezalel, 1986. "A proof that the core of an ordinal convex game is a von Neumann-Morgenstern solution," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 83-87, February.
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    Cited by:

    1. J. Zambujal-Oliveira, 2021. "Supply Chain Innovation Research: A Conceptual Approach of Information Management with Game Theory," Group Decision and Negotiation, Springer, vol. 30(2), pages 377-394, April.
    2. Michel Grabisch & Hervé Moulin & José Manuel Zarzuelo, 2024. "Professor Peter Sudhölter (1957–2024)," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 289-294, June.

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    More about this item

    Keywords

    NTU game; Convex game; Bargaining set;
    All these keywords.

    JEL classification:

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

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