Games induced by the partitioning of a graph
AbstractThe 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.
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Bibliographic InfoPaper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00830291.
Date of creation: 29 Aug 2012
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Publication status: Published, Annals of Operations Research, 2012, 201, 1, 229-249
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Communication networks; Coalition structure; Cooperative game; Strength of a graph;
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- van den Nouweland, Anne & Borm, Peter, 1991.
"On the Convexity of Communication Games,"
International Journal of Game Theory,
Springer, vol. 19(4), pages 421-30.
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