Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations

Takayuki Oishi, Mikio Nakayama, Toru Hokari, Yukihiko Funaki

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    In this paper, for each solution for TU games, we define its "dual" and "anti-dual". Then, we apply these notions to axioms: two axioms are (anti-)dual to each other if whenever a solution satisfies one of them, its (anti-)dual satisfies the other. It turns out that these definitions allow us not only to organize existing axiomatizations of various solutions but also to find new axiomatizations of some solutions. As an illustration, we show that two well-known axiomatizations of the core are essentially equivalent in the sense that one can be derived from the other, and derive new axiomatizations of the Shapley value and the Dutta-Ray solution.

    Original languageEnglish
    Pages (from-to)44-53
    Number of pages10
    JournalJournal of Mathematical Economics
    Volume63
    DOIs
    Publication statusPublished - 2016 Mar 1

    Fingerprint

    TU Game
    Axiomatization
    Axioms
    Duality
    Shapley Value
    Half line
    TU game
    Serious games

    Keywords

    • Anti-duality
    • Core
    • Duality
    • Dutta-Ray solution
    • Shapley value

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Applied Mathematics

    Cite this

    Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations. / Oishi, Takayuki; Nakayama, Mikio; Hokari, Toru; Funaki, Yukihiko.

    In: Journal of Mathematical Economics, Vol. 63, 01.03.2016, p. 44-53.

    Research output: Contribution to journalArticle

    @article{1cbe899f7b874dd583dfe8fb370850bd,
    title = "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations",
    abstract = "In this paper, for each solution for TU games, we define its {"}dual{"} and {"}anti-dual{"}. Then, we apply these notions to axioms: two axioms are (anti-)dual to each other if whenever a solution satisfies one of them, its (anti-)dual satisfies the other. It turns out that these definitions allow us not only to organize existing axiomatizations of various solutions but also to find new axiomatizations of some solutions. As an illustration, we show that two well-known axiomatizations of the core are essentially equivalent in the sense that one can be derived from the other, and derive new axiomatizations of the Shapley value and the Dutta-Ray solution.",
    keywords = "Anti-duality, Core, Duality, Dutta-Ray solution, Shapley value",
    author = "Takayuki Oishi and Mikio Nakayama and Toru Hokari and Yukihiko Funaki",
    year = "2016",
    month = "3",
    day = "1",
    doi = "10.1016/j.jmateco.2015.12.005",
    language = "English",
    volume = "63",
    pages = "44--53",
    journal = "Journal of Mathematical Economics",
    issn = "0304-4068",
    publisher = "Elsevier",

    }

    TY - JOUR

    T1 - Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations

    AU - Oishi, Takayuki

    AU - Nakayama, Mikio

    AU - Hokari, Toru

    AU - Funaki, Yukihiko

    PY - 2016/3/1

    Y1 - 2016/3/1

    N2 - In this paper, for each solution for TU games, we define its "dual" and "anti-dual". Then, we apply these notions to axioms: two axioms are (anti-)dual to each other if whenever a solution satisfies one of them, its (anti-)dual satisfies the other. It turns out that these definitions allow us not only to organize existing axiomatizations of various solutions but also to find new axiomatizations of some solutions. As an illustration, we show that two well-known axiomatizations of the core are essentially equivalent in the sense that one can be derived from the other, and derive new axiomatizations of the Shapley value and the Dutta-Ray solution.

    AB - In this paper, for each solution for TU games, we define its "dual" and "anti-dual". Then, we apply these notions to axioms: two axioms are (anti-)dual to each other if whenever a solution satisfies one of them, its (anti-)dual satisfies the other. It turns out that these definitions allow us not only to organize existing axiomatizations of various solutions but also to find new axiomatizations of some solutions. As an illustration, we show that two well-known axiomatizations of the core are essentially equivalent in the sense that one can be derived from the other, and derive new axiomatizations of the Shapley value and the Dutta-Ray solution.

    KW - Anti-duality

    KW - Core

    KW - Duality

    KW - Dutta-Ray solution

    KW - Shapley value

    UR - http://www.scopus.com/inward/record.url?scp=84962565696&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84962565696&partnerID=8YFLogxK

    U2 - 10.1016/j.jmateco.2015.12.005

    DO - 10.1016/j.jmateco.2015.12.005

    M3 - Article

    AN - SCOPUS:84962565696

    VL - 63

    SP - 44

    EP - 53

    JO - Journal of Mathematical Economics

    JF - Journal of Mathematical Economics

    SN - 0304-4068

    ER -