Games induced by the partitioning of a graph

Michel Grabisch (1, 2) , Alexandre Skoda (1)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics

The paper aims at generalizing the notion of restricted game on a communication graph, introduced by Myerson. We consider communication graphs with weighted edges, and we define arbitrary ways of partitioning any subset of a graph, which we call correspondences. A particularly useful way to partition a graph is obtained by computing the strength of the graph. The strength of a graph is a measure introduced in graph theory to evaluate the resistance of networks under attacks, and it provides a natural partition of the graph (called the Gusfield correspondence) into resistant components. We perform a general study of the inheritance of superadditivity and convexity for the restricted game associated with a given correspondence. Our main result is to give for cycle-free graphs necessary and sufficient conditions for the inheritance of convexity of the restricted game associated with the Gusfield correspondence.

Mots clés: Communication networks; Coalition structure; Cooperative game; Strength of a graph

Domaines: Mathématique discrète [cs.DM]; Economies et finances; Informatique et théorie des jeux [cs.GT]; Recherche opérationnelle [math.OC]

Michel Grabisch, Alexandre Skoda. Games induced by the partitioning of a graph. Annals of Operations Research, 2012, 201 (1), pp.229-249. ⟨10.1007/s10479-012-1200-8⟩. ⟨hal-00830291⟩