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The Projective Core of Symmetric Games with Externalities

Author

Listed:
  • Takaaki Abe

    (Graduate School of Economics, Waseda University)

  • Yukihiko Funaki

    (School of Political Science and Economics, Waseda University)

Abstract
The purpose of this paper is to analyze stable distributions and coalition structures in certain economic situations. We consider the projective core as the most myopic core of the cores defined for games with externalities. Although the core is often defined only for the grand coalition, we define the projective core for each coalition structure and apply it to some economic models such as the public goods game, the Cournot oligopoly, and the common pool resource game. Moreover, we formulate the Bertrand oligopoly as a game with externalities. We argue that symmetry is a common property of these models in terms of the partition function. We offer some general results that hold for all symmetric games with externalities and discuss the implications of the economic models. We also provide necessary and sufficient conditions for the projective core of the models to be nonempty.

Suggested Citation

  • Takaaki Abe & Yukihiko Funaki, 2018. "The Projective Core of Symmetric Games with Externalities," Working Papers 1809, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1809
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    References listed on IDEAS

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    9. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
    10. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    11. Takaaki Abe & Yukihiko Funaki, 2017. "The non-emptiness of the core of a partition function form game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 715-736, August.
    12. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 37-44.
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    Cited by:

    1. Yang, Guangjing & Sun, Hao, 2023. "The recursive nucleolus for partition function form games," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    2. Giorgos Stamatopoulos, 2020. "On the $$\gamma $$γ-core of asymmetric aggregative games," Theory and Decision, Springer, vol. 88(4), pages 493-504, May.

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    More about this item

    Keywords

    Core; Externalities; Oligopoly; Public goods;
    All these keywords.

    JEL classification:

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

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