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Decomposing a balanced game: A necessary and sufficient condition for the nonemptiness of the core

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  • Abe, Takaaki

Abstract

The Bondareva–Shapley condition is the most eminent necessary and sufficient condition for the core of a transferable utility game to be nonempty. In this paper, we provide a new necessary and sufficient condition. We show that a game has a nonempty core if and only if the game can be decomposed into some simple games.

Suggested Citation

  • Abe, Takaaki, 2019. "Decomposing a balanced game: A necessary and sufficient condition for the nonemptiness of the core," Economics Letters, Elsevier, vol. 176(C), pages 9-13.
    • Handle: RePEc:eee:ecolet:v:176:y:2019:i:c:p:9-13
    DOI: 10.1016/j.econlet.2018.12.009
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    References listed on IDEAS

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    1. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    2. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    3. 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.
    4. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
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    Cited by:

    1. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).

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    More about this item

    Keywords

    Cooperative game; Core; Decomposition;
    All these keywords.

    JEL classification:

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

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