Inheritance of Convexity for the 𝒫̃_min-Restricted Game
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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 𝒫̃_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 𝒫̃_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 𝒫̃_min.
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