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Stable Cooperation in a Game with a Major Player

Author

Listed:
  • Elena Parilina

    (Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia)

  • Artem Sedakov

    (Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia)

Abstract

The theory of cooperative games with restricted cooperation has been rapidly developing over the last decades. In our study, we present a special game with restricted cooperation — a game with a major player — a modified version of the landlord game presented in Moulin [1988]. Cooperation of players is supposed to be restricted by a communication structure (a star-graph) as well as a coalition structure. We adopt two well-known cooperative allocations — the Myerson value and the ES-value — to the case when there exist restrictions on the cooperation of players and provide their analytical expressions. Additionally, we examine stability of coalition structures using the concept of the Nash equilibrium and formulate conditions guaranteeing such stability for a given coalition structure.

Suggested Citation

  • Elena Parilina & Artem Sedakov, 2016. "Stable Cooperation in a Game with a Major Player," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-20, June.
    • Handle: RePEc:wsi:igtrxx:v:18:y:2016:i:02:n:s0219198916400053
    DOI: 10.1142/S0219198916400053
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    References listed on IDEAS

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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
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    6. Vazquez-Brage, Margarita & Garcia-Jurado, Ignacio & Carreras, Francesc, 1996. "The Owen Value Applied to Games with Graph-Restricted Communication," Games and Economic Behavior, Elsevier, vol. 12(1), pages 42-53, January.
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    9. Elena Parilina & Artem Sedakov, 2014. "Stable Bank Cooperation for Cost Reduction Problem," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(1), pages 7-25, August.
    10. Andreas Tutic, 2010. "The Aumann-Drèze Value, The Wiese Value, And Stability: A Note," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 189-195.
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    Cited by:

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    2. Vladimir Mazalov & Elena Parilina, 2020. "The Euler-Equation Approach in Average-Oriented Opinion Dynamics," Mathematics, MDPI, vol. 8(3), pages 1-16, March.

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    More about this item

    Keywords

    Coalition structure; graph; restricted cooperation; Myerson value; ES-value; stability;
    All these keywords.

    JEL classification:

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

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