Games induced by the partitioning of a graph

Journal article: 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.

Author(s)

Michel Grabisch, Alexandre Skoda

Journal
  • Annals of Operations Research
Date of publication
  • 2012
Keywords JEL
C71
Keywords
  • Communication networks
  • Coalition structure
  • Cooperative game
  • Strength of a graph
Pages
  • 229-249
Version
  • 1
Volume
  • 201