Reconciling marginalism with egalitarianism: Consistency, monotonicity, and implementation of egalitarian Shapley values

René van den Brink, Yukihiko Funaki, Yuan Ju

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    39 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

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    ASJC Scopus subject areas

    • Economics and Econometrics
    • Social Sciences (miscellaneous)

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