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Sharing a collective probability of success

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  • Dehez, Pierre

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

Abstract

How to allocate the probability of success resulting from the joint actions of a group of players? To address this question, Hou et al. (Operations Research Letters 46, 2018) propose to use the Shapley value of a transferable utility game, a "probability game" assuming probabilistic independence. The purpose of the present note is to analyze the properties of probability games and their duals and to study various solution concepts, in particular the core and the Shapley value. We give an axiomatic foundation of the Shapley value on the class of probability games and we investigate the link between different solution concepts, including asymmetric values.

Suggested Citation

  • Dehez, Pierre, 2020. "Sharing a collective probability of success," LIDAM Discussion Papers CORE 2020035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2020035
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    References listed on IDEAS

    as
    1. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    2. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2022. "Optimal Management of Evolving Hierarchies," Management Science, INFORMS, vol. 68(8), pages 6024-6038, August.
    3. Samuel Ferey & Pierre Dehez, 2016. "Multiple Causation, Apportionment, and the Shapley Value," The Journal of Legal Studies, University of Chicago Press, vol. 45(1), pages 143-171.
    4. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
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    6. 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).
    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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. 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.
    10. Fatma Aslan & Papatya Duman & Walter Trockel, 2019. "Duality for General TU-games Redefined," Working Papers CIE 121, Paderborn University, CIE Center for International Economics.
    11. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.
    12. Zhao, Jingang, 2018. "Three little-known and yet still significant contributions of Lloyd Shapley," Games and Economic Behavior, Elsevier, vol. 108(C), pages 592-599.
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