Marginal games and characterizations of the shapley value in TU games

Takumi Kongo, Yukihiko Funaki

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Axiomatizations and recursive representations of the Shapley value on the class of all cooperative games with transferable utilities are given. Marginal games, which are closely related to dual games, play central roles in our results. Our axiomatizations are based on axioms that are marginal game variations of the well-known balanced contributions property, so that they are interpreted as fair treatment between two players in games as the balanced contributions property is. Our general recursive representation enables us to represent the Shapley value for n-person games by those for r-person and (n − r)-person games with fixed r < n. The particular case of r = 1 has a clear contrasting interpretation to the existing recursive formula.

    Original languageEnglish
    Title of host publicationGame Theory and Applications - 3rd Joint China-Dutch Workshop and 7th China Meeting, GTA 2016, Revised Selected Papers
    PublisherSpringer Verlag
    Pages165-173
    Number of pages9
    Volume758
    ISBN (Print)9789811067525
    DOIs
    Publication statusPublished - 2017
    Event3rd Joint China-Dutch Workshop on Game Theory and Applications and 7th China Meeting on Game Theory and Applications, GTA 2016 - Fuzhou, China
    Duration: 2016 Nov 202016 Nov 23

    Publication series

    NameCommunications in Computer and Information Science
    Volume758
    ISSN (Print)1865-0929

    Other

    Other3rd Joint China-Dutch Workshop on Game Theory and Applications and 7th China Meeting on Game Theory and Applications, GTA 2016
    CountryChina
    CityFuzhou
    Period16/11/2016/11/23

    Keywords

    • Balanced contribution
    • Dual game
    • Marginal game
    • Recursive representation
    • Shapley value

    ASJC Scopus subject areas

    • Computer Science(all)
    • Mathematics(all)

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  • Cite this

    Kongo, T., & Funaki, Y. (2017). Marginal games and characterizations of the shapley value in TU games. In Game Theory and Applications - 3rd Joint China-Dutch Workshop and 7th China Meeting, GTA 2016, Revised Selected Papers (Vol. 758, pp. 165-173). (Communications in Computer and Information Science; Vol. 758). Springer Verlag. https://doi.org/10.1007/978-981-10-6753-2_12