Games induced by the partitioning of a graph

Michel Grabisch and A. Skoda ()

Annals of Operations Research, 2012, vol. 201, issue 1, 229-249

Abstract: 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. Copyright Springer Science+Business Media, LLC 2012

Keywords: Communication networks; Coalition structure; Cooperative game; Strength of a graph (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (22)

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Working Paper: Games induced by the partitioning of a graph (2012)
Working Paper: Games induced by the partitioning of a graph (2012)
Working Paper: Games induced by the partitioning of a graph (2012)
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DOI: 10.1007/s10479-012-1200-8

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