The uniqueness of a reduced game in a characterization of the core in terms of consistency

Yukihiko Funaki, Takehiko Yamato

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    In this paper, we examine the uniqueness of a reduced game in an axiomatic characterization of the core of transferable utility (TU) games in terms of consistency. Tadenuma [10] establishes that the core is the only solution satisfying non-emptiness, individual rationality, and consistency with respect to a natural reduced game due to Moulin [6]. However, the core satisfies consistency with respect to many other reduced games, including unnatural ones. Then we ask whether there are other reduced games that can be used to characterize the core based on the same three axioms. The answer is no: the Moulin reduced game is the only reduced game such that the core is characterized by the three axioms, since for any other reduced game, there is a solution that satisfies the three axioms, but it differs from the core. Many other unnatural reduced games cannot be used to characterize the core based on the three axioms. Funaki [4] provides another axiomatization of the core: the core is the only solution satisfying non-emptiness, Pareto optimality, sub-grand rationality, and consistency with respect to a simple reduced game similar to a so-called subgame. We show that the simple reduced game is the only reduced game that can be used to characterize the core by the four axioms.

    Original languageEnglish
    Title of host publicationAnnals of the International Society of Dynamic Games
    PublisherBirkhauser
    Pages147-162
    Number of pages16
    DOIs
    Publication statusPublished - 2006 Jan 1

    Publication series

    NameAnnals of the International Society of Dynamic Games
    Volume8
    ISSN (Print)2474-0179
    ISSN (Electronic)2474-0187

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Statistics and Probability
    • Applied Mathematics

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  • Cite this

    Funaki, Y., & Yamato, T. (2006). The uniqueness of a reduced game in a characterization of the core in terms of consistency. In Annals of the International Society of Dynamic Games (pp. 147-162). (Annals of the International Society of Dynamic Games; Vol. 8). Birkhauser. https://doi.org/10.1007/0-8176-4501-2_8