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How outside options are incorporated into payoff distributions

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  • Takaaki Abe

Abstract

This paper examines how outside options are incorporated into payoff distributions in games with coalition structures. We introduce and characterize the alpha-value, which "fully" incorporates outside options, and provide a new characterization of the Aumann-Dreze value as an allocation rule that does not incorporate outside options. We show that the chi-value (Casajus, 2009) is a component-wise convex combination of these two values and thus incorporates outside options in a discounted form.

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  • Takaaki Abe, 2026. "How outside options are incorporated into payoff distributions," Papers 2609.00799, arXiv.org.
    • Handle: RePEc:arx:papers:2609.00799
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    References listed on IDEAS

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    1. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    2. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
    3. Yoshio Kamijo & Takumi Kongo, 2010. "Axiomatization of the Shapley value using the balanced cycle contributions property," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 563-571, October.
    4. Abe, Takaaki, 2021. "Stability and values for games with coalition structures," Economics Letters, Elsevier, vol. 200(C).
    5. Harald Wiese, 2007. "Measuring The Power Of Parties Within Government Coalitions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 307-322.
    6. Andreas Tutic & Stefan Pfau & André Casajus, 2011. "Experiments on bilateral bargaining in markets," Theory and Decision, Springer, vol. 70(4), pages 529-546, April.
    7. Abe, Takaaki, 2024. "Equal surplus sharing values for games with coalition structures," Economics Letters, Elsevier, vol. 240(C).
    8. Takumi Kongo, 2024. "Equal support from others for unproductive players: efficient and linear values that satisfy the equal treatment and weak null player out properties for cooperative games," Annals of Operations Research, Springer, vol. 338(2), pages 973-989, July.
    9. Casajus, André & La Mura, Pierfrancesco, 2024. "Null players, outside options, and stability: The conditional Shapley value," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    10. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
    11. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
    12. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Casajus, André & Tutić, Andreas, 2013. "Nash bargaining, Shapley threats, and outside options," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 262-267.
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