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New characterizations for largeness of the core

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  • Estévez-Fernández, Arantza

Abstract

In this paper, we provide three new characterizations of largeness of the core. The first characterization is based on minimal covers of the grand coalition and associated inequalities. The second characterization shows the relation between the bases that provide core elements of the game and the bases that provide core elements of the games that are obtained from the original one by increasing the value of the grand coalition. The third characterization is based on the idea that if a base of the grand coalition does not provide a core element of the game, it should not provide a core element of a game which differs from the original one only by an increase of the value of the grand coalition. Based on these new characterizations, we show the equivalence between largeness of the core and stability of the core for games with at most 5 players.

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  • Estévez-Fernández, Arantza, 2012. "New characterizations for largeness of the core," Games and Economic Behavior, Elsevier, vol. 76(1), pages 160-180.
    • Handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:160-180
    DOI: 10.1016/j.geb.2012.04.003
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    More about this item

    Keywords

    Core; Upper core; Largeness of the core; Stability;
    All these keywords.

    JEL classification:

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

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