Weighted Average-convexity and Cooperative Games

Alexandre Skoda () and Xavier Venel ()
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Alexandre Skoda: UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Xavier Venel: Dipartimento di Economia e Finanza [Roma] - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]

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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.

Keywords: TU-games; convexity; average-convexity; weighted Shapley value; communication (search for similar items in EconPapers)
Date: 2022-06-27
New Economics Papers: this item is included in nep-gth
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Published in 2022

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