Weak differential marginality and the Shapley value

André Casajus, Koji Yokote

    Research output: Contribution to journal › Article

    6 Citations (Scopus)

    Abstract

    The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ marginal contributions to coalitions containing neither of them does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show that this characterization can be improved by using a substantially weaker property than differential marginality. Weak differential marginality requires two players’ payoffs to change in the same direction when these players’ marginal contributions to coalitions containing neither of them change by the same amount.

    Original languageEnglish
    Pages (from-to)274-284
    Number of pages11
    JournalJournal of Economic Theory
    Volume167
    DOIs
    Publication statusPublished - 2017 Jan 1

    Fingerprint

    Shapley value
    Marginality
    Marginal contribution
    Cooperative game

    Keywords

    • Differential marginality
    • Shapley value
    • TU game
    • Weak differential marginality

    ASJC Scopus subject areas

    • Economics and Econometrics

    Cite this

    Weak differential marginality and the Shapley value. / Casajus, André; Yokote, Koji.

    In: Journal of Economic Theory, Vol. 167, 01.01.2017, p. 274-284.

    Research output: Contribution to journal › Article

    Casajus, A & Yokote, K 2017, 'Weak differential marginality and the Shapley value', Journal of Economic Theory, vol. 167, pp. 274-284. https://doi.org/10.1016/j.jet.2016.11.007
    Casajus A, Yokote K. Weak differential marginality and the Shapley value. Journal of Economic Theory. 2017 Jan 1;167:274-284. https://doi.org/10.1016/j.jet.2016.11.007
    Casajus, André ; Yokote, Koji. / Weak differential marginality and the Shapley value. In: Journal of Economic Theory. 2017 ; Vol. 167. pp. 274-284.
    @article{889cd68ac7ea4bcb9de3fab7f72bfaa7,
    title = "Weak differential marginality and the Shapley value",
    abstract = "The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ marginal contributions to coalitions containing neither of them does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show that this characterization can be improved by using a substantially weaker property than differential marginality. Weak differential marginality requires two players’ payoffs to change in the same direction when these players’ marginal contributions to coalitions containing neither of them change by the same amount.",
    keywords = "Differential marginality, Shapley value, TU game, Weak differential marginality",
    author = "Andr{\'e} Casajus and Koji Yokote",
    year = "2017",
    month = "1",
    day = "1",
    doi = "10.1016/j.jet.2016.11.007",
    language = "English",
    volume = "167",
    pages = "274--284",
    journal = "Journal of Economic Theory",
    issn = "0022-0531",
    publisher = "Academic Press Inc.",

    }

    TY - JOUR

    T1 - Weak differential marginality and the Shapley value

    AU - Casajus, André

    AU - Yokote, Koji

    PY - 2017/1/1

    Y1 - 2017/1/1

    N2 - The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ marginal contributions to coalitions containing neither of them does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show that this characterization can be improved by using a substantially weaker property than differential marginality. Weak differential marginality requires two players’ payoffs to change in the same direction when these players’ marginal contributions to coalitions containing neither of them change by the same amount.

    AB - The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ marginal contributions to coalitions containing neither of them does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show that this characterization can be improved by using a substantially weaker property than differential marginality. Weak differential marginality requires two players’ payoffs to change in the same direction when these players’ marginal contributions to coalitions containing neither of them change by the same amount.

    KW - Differential marginality

    KW - Shapley value

    KW - TU game

    KW - Weak differential marginality

    UR - http://www.scopus.com/inward/record.url?scp=85008616128&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85008616128&partnerID=8YFLogxK

    U2 - 10.1016/j.jet.2016.11.007

    DO - 10.1016/j.jet.2016.11.007

    M3 - Article

    AN - SCOPUS:85008616128

    VL - 167

    SP - 274

    EP - 284

    JO - Journal of Economic Theory

    JF - Journal of Economic Theory

    SN - 0022-0531

    ER -

    Access to Document