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Weighted average-convexity and Shapley values

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  • Skoda, Alexandre
  • Venel, Xavier

Abstract

We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. Our main result is that if a game is weighted average-convex, then the corresponding weighted Shapley value is in the core.

Suggested Citation

  • Skoda, Alexandre & Venel, Xavier, 2023. "Weighted average-convexity and Shapley values," Games and Economic Behavior, Elsevier, vol. 140(C), pages 88-98.
    • Handle: RePEc:eee:gamebe:v:140:y:2023:i:c:p:88-98
    DOI: 10.1016/j.geb.2023.02.008
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    References listed on IDEAS

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    1. 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.
    2. Inarra, Elena & Usategui, Jose M, 1993. "The Shapley Value and Average Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(1), pages 13-29.
    3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    4. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
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    Cited by:

    1. Alexandre Skoda & Xavier Venel, 2025. "Inheritance of weighted average-convexity in communication situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(1), pages 1-33, June.
    2. Bahel, Eric & Trudeau, Christian & Wang, Haoyu, 2026. "Preconvex games," Games and Economic Behavior, Elsevier, vol. 155(C), pages 250-266.

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