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Inheritance of Convexity for the P˜min-Restricted Game

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.
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https://halshs.archives-ouvertes.fr/halshs-02967120
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Submitted on : Wednesday, October 14, 2020 - 4:45:58 PM
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Alexandre Skoda. Inheritance of Convexity for the P˜min-Restricted Game. 2020. ⟨halshs-02967120⟩

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