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1-convex transferable utility games, a reappraisal

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  • Dehez, Pierre

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

1-convex games have been introduced by Theo Driessen in his 1985 PhD dissertation. They form an interesting class of games for at least one reason: the core of a 1-convex n-player game is a regular simplex of dimension n – 1 or a single point. As a consequence, its nucleolus is the center of gravity of the core. We recall and extend the results obtained by Driessen and provide examples and applications.

Suggested Citation

  • Dehez, Pierre, 2021. "1-convex transferable utility games, a reappraisal," LIDAM Discussion Papers CORE 2021016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2021016
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    References listed on IDEAS

    as
    1. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    2. Dehez Pierre & Poukens Sophie, 2014. "The Shapley Value as a Guide to FRAND Licensing Agreements," Review of Law & Economics, De Gruyter, vol. 10(3), pages 1-20, November.
    3. Pierre Dehez, 2013. "Cooperative provision of indivisible public goods," Theory and Decision, Springer, vol. 74(1), pages 13-29, January.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Driessen, T. & Tijs, S.H., 1983. "The t-value, the nucleolus and the core for a subclass of games," Other publications TiSEM 73fdfe73-c88c-4a9f-8ee7-c, Tilburg University, School of Economics and Management.
    6. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    7. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    8. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    9. Anna Khmelnitskaya & Theo Driessen, 2017. "A Comment on Dehez and Tellone, “Data games: sharing public goods with exclusion”," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(1), pages 264-265, February.
    10. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
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    More about this item

    Keywords

    Transferable utility games ; core ; nucleolus ; Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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