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.(c) 2023 Elsevier Inc. All rights reserved.
Weighted average-convexity and Shapley values / Skoda, A; Venel, Xavier Mathieu Raymond. - In: GAMES AND ECONOMIC BEHAVIOR. - ISSN 0899-8256. - 140:(2023), pp. 88-98. [10.1016/j.geb.2023.02.008]
Weighted average-convexity and Shapley values
Venel, X
2023
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.(c) 2023 Elsevier Inc. All rights reserved.
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