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Nonemptiness of the f-Core Without Comprehensiveness

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Listed:
  • Hideo Konishi

    (Boston College)

  • Dimitar Simeonov

    (Bahçeşehir University)

Abstract

Kaneko and Wooders (1986) showed under general conditions that an atomless NTU game with finite types of players has a core allocation when coalitions have a finite number of players. In this paper, we provide a direct proof of the above result using Kakutani’s fixed point theorem when the sizes of coalitions are not only finite but also bounded above. This condition simplifies the presentation of the model and the existence proof. Most importantly, we can drop the comprehensiveness assumption, allowing for a much wider applicability of the result for matching problems, as well as for hedonic coalition formation problems. Additionally, without comprehensiveness, f-core allocations might not possess equal-treatment in payoffs for the same type. We also note that the nonemptiness of the core of NTU games by Scarf (1971) can be derived from our result as a corollary.

Suggested Citation

  • Hideo Konishi & Dimitar Simeonov, 2023. "Nonemptiness of the f-Core Without Comprehensiveness," Boston College Working Papers in Economics 1062, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:1062
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    References listed on IDEAS

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    More about this item

    Keywords

    f-core; comprehensiveness; atomless players;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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