Inheritance of Convexity for the P˜min-Restricted Game

Alexandre Skoda (alexandre.skoda@univ-paris1.fr)
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Alexandre Skoda: Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.cnrs.fr

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

Abstract: We consider a restricted game on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components obtained with a specific partition P˜min. This partition relies on the same principle as the partition P˜min introduced by Grabisch and Skoda (2012) but restricted to connected coalitions. More precisely, this new partition P˜min is induced by the deletion of the minimum weight edges in each connected component associated with a coalition. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with P˜min

Keywords: Cooperative game; convexity; graph-restricted game; graph partitions (search for similar items in EconPapers)
Pages: 37 pages
Date: 2020-09
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (2)

Published in Mathematical Methods of Operations Research, Springer Verlag, 93, 2021, pp. 1–32

Downloads: (external link)
http://mse.univ-paris1.fr/pub/mse/CES2020/20020.pdf (application/pdf)
https://halshs.archives-ouvertes.fr/halshs-02967120
https://doi.org/10.1007/s00186-020-00728-4
https://arxiv.org/abs/1708.02675v3

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