Weighted Average-convexity and Cooperative Games

Alexandre Skoda () and Xavier Venel ()
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Alexandre Skoda: Université Paris 1 Panthéon-Sorbonne, Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.cnrs.fr
Xavier Venel: LUISS - Dipartimento di Economia e Finanza

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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. First, we prove that if a game is weighted average-convex, then the corresponding weighted Shapley value is in the core. Second, we exhibit necessary conditions for a communication TU-game to preserve the weighted average-convexity. 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)
Pages: 54 pages
Date: 2022-06
New Economics Papers: this item is included in nep-gth
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http://mse.univ-paris1.fr/pub/mse/CES2022/22016.pdf (application/pdf)
https://shs.hal.science/halshs-03717539

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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:22016

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