Reconciling marginalism with egalitarianism

Consistency, monotonicity, and implementation of egalitarian Shapley values

René van den Brink, Yukihiko Funaki, Yuan Ju

    Research output: Contribution to journalArticle

    36 Citations (Scopus)

    Abstract

    One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism.

    Original languageEnglish
    Pages (from-to)693-714
    Number of pages22
    JournalSocial Choice and Welfare
    Volume40
    Issue number3
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    egalitarianism
    economics
    Monotonicity
    Marginalism
    Shapley value
    Egalitarianism
    Trade-offs

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Social Sciences (miscellaneous)

    Cite this

    Reconciling marginalism with egalitarianism : Consistency, monotonicity, and implementation of egalitarian Shapley values. / van den Brink, René; Funaki, Yukihiko; Ju, Yuan.

    In: Social Choice and Welfare, Vol. 40, No. 3, 2013, p. 693-714.

    Research output: Contribution to journalArticle

    @article{fa25f0c754c24c7a84a428b5691e6627,
    title = "Reconciling marginalism with egalitarianism: Consistency, monotonicity, and implementation of egalitarian Shapley values",
    abstract = "One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism.",
    author = "{van den Brink}, Ren{\'e} and Yukihiko Funaki and Yuan Ju",
    year = "2013",
    doi = "10.1007/s00355-011-0634-2",
    language = "English",
    volume = "40",
    pages = "693--714",
    journal = "Social Choice and Welfare",
    issn = "0176-1714",
    publisher = "Springer New York",
    number = "3",

    }

    TY - JOUR

    T1 - Reconciling marginalism with egalitarianism

    T2 - Consistency, monotonicity, and implementation of egalitarian Shapley values

    AU - van den Brink, René

    AU - Funaki, Yukihiko

    AU - Ju, Yuan

    PY - 2013

    Y1 - 2013

    N2 - One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism.

    AB - One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism.

    UR - http://www.scopus.com/inward/record.url?scp=84872595918&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84872595918&partnerID=8YFLogxK

    U2 - 10.1007/s00355-011-0634-2

    DO - 10.1007/s00355-011-0634-2

    M3 - Article

    VL - 40

    SP - 693

    EP - 714

    JO - Social Choice and Welfare

    JF - Social Choice and Welfare

    SN - 0176-1714

    IS - 3

    ER -