Weighted values and the core in NTU games

    Research output: Contribution to journalArticle

    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

    Fingerprint

    NTU Games
    Shapley Value
    Grand Coalition
    game theory
    aggregation
    edition
    TU Game
    Values
    Coalitions
    Game Theory
    Expected Value
    Half-space
    Aggregation
    Closure
    Closed
    NTU games
    Relationships
    Marginal contribution
    Egalitarian solution
    Shapley value

    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

    Cite this

    Weighted values and the core in NTU games. / Yokote, Koji.

    In: International Journal of Game Theory, Vol. 46, No. 3, 01.08.2017, p. 631-654.

    Research output: Contribution to journalArticle

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