Inheritance of Convexity for the P˜min-Restricted Game

Alexandre Skoda (1, 2)

1 UP1 - Université Paris 1 Panthéon-Sorbonne
2 CES - Centre d'économie de la Sorbonne

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.

Mots clés: graph-restricted game; convexity; cooperative game; graph partitions

Domaines: Economies et finances; Recherche opérationnelle [cs.RO]

Alexandre Skoda. Inheritance of Convexity for the P˜min-Restricted Game. 2020. ⟨halshs-02967120⟩