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

    Fingerprint

    Uniqueness
    Game
    Axioms
    Rationality
    Reduced game
    Pareto Optimality
    Axiomatization

    ASJC Scopus subject areas

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

    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

    The uniqueness of a reduced game in a characterization of the core in terms of consistency. / Funaki, Yukihiko; Yamato, Takehiko.

    Annals of the International Society of Dynamic Games. Birkhauser, 2006. p. 147-162 (Annals of the International Society of Dynamic Games; Vol. 8).

    Research output: Chapter in Book/Report/Conference proceedingChapter

    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. Annals of the International Society of Dynamic Games, vol. 8, Birkhauser, pp. 147-162. https://doi.org/10.1007/0-8176-4501-2_8
    Funaki Y, Yamato T. 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. Birkhauser. 2006. p. 147-162. (Annals of the International Society of Dynamic Games). https://doi.org/10.1007/0-8176-4501-2_8
    Funaki, Yukihiko ; Yamato, Takehiko. / The uniqueness of a reduced game in a characterization of the core in terms of consistency. Annals of the International Society of Dynamic Games. Birkhauser, 2006. pp. 147-162 (Annals of the International Society of Dynamic Games).
    @inbook{60003624f5c84c899a329d0f0d46cc5b,
    title = "The uniqueness of a reduced game in a characterization of the core in terms of consistency",
    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.",
    author = "Yukihiko Funaki and Takehiko Yamato",
    year = "2006",
    month = "1",
    day = "1",
    doi = "10.1007/0-8176-4501-2_8",
    language = "English",
    series = "Annals of the International Society of Dynamic Games",
    publisher = "Birkhauser",
    pages = "147--162",
    booktitle = "Annals of the International Society of Dynamic Games",

    }

    TY - CHAP

    T1 - The uniqueness of a reduced game in a characterization of the core in terms of consistency

    AU - Funaki, Yukihiko

    AU - Yamato, Takehiko

    PY - 2006/1/1

    Y1 - 2006/1/1

    N2 - 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.

    AB - 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.

    UR - http://www.scopus.com/inward/record.url?scp=85054564232&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85054564232&partnerID=8YFLogxK

    U2 - 10.1007/0-8176-4501-2_8

    DO - 10.1007/0-8176-4501-2_8

    M3 - Chapter

    T3 - Annals of the International Society of Dynamic Games

    SP - 147

    EP - 162

    BT - Annals of the International Society of Dynamic Games

    PB - Birkhauser

    ER -