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Inheritance of Convexity for the P˜min-Restricted Game

Alexandre Skoda ()
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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

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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; graph partitions; convexity; graph-restricted game (search for similar items in EconPapers)
Date: 2020-09
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-02967120
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Published in 2020

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