Weighted values and the core in NTU games

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    1 Citation (Scopus)

    Abstract

    Monderer et al. (Int J Game Theory 21(1):27–39, 1992) proved that the core is included in the set of the weighted Shapley values in TU games. The purpose of this paper is to extend this result to NTU games. We first show that the core is included in the closure of the positively weighted egalitarian solutions introduced by Kalai and Samet (Econometrica 53(2):307–327, 1985). Next, we show that the weighted version of the Shapley NTU value by Shapley (La Decision, aggregation et dynamique des ordres de preference, Editions du Centre National de la Recherche Scientifique, Paris, pp 251–263, 1969) does not always include the core. These results indicate that, in view of the relationship to the core, the egalitarian solution is a more desirable extension of the weighted Shapley value to NTU games. As a byproduct of our approach, we also clarify the relationship between the core and marginal contributions in NTU games. We show that, if the attainable payoff for the grand coalition is represented as a closed-half space, then any element of the core is attainable as the expected value of marginal contributions.

    Original languageEnglish
    Pages (from-to)631-654
    Number of pages24
    JournalInternational Journal of Game Theory
    Volume46
    Issue number3
    DOIs
    Publication statusPublished - 2017 Aug 1

    Keywords

    • Core
    • Marginal contribution
    • NTU game
    • Shapley NTU value
    • Weighted egalitarian solution

    ASJC Scopus subject areas

    • Statistics and Probability
    • Mathematics (miscellaneous)
    • Social Sciences (miscellaneous)
    • Economics and Econometrics
    • Statistics, Probability and Uncertainty

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