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Weighted Average-convexity and Cooperative Games

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 averageconvexity and cooperative games. First, we prove that if a game is weighted averageconvex, then the corresponding weighted Shapley value is in the core. Second, we exhibit necessary conditions for a communication TU-game to preserve the weighted averageconvexity. Finally, we provide a complete characterization when the underlying graph is a priority decreasing tree.
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https://halshs.archives-ouvertes.fr/halshs-03717539
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Submitted on : Friday, July 8, 2022 - 11:36:33 AM
Last modification on : Thursday, July 14, 2022 - 3:28:38 AM

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  • HAL Id : halshs-03717539, version 1

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Alexandre Skoda, Xavier Venel. Weighted Average-convexity and Cooperative Games. 2022. ⟨halshs-03717539⟩

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