Convexity of Network Restricted Games Induced by Minimum PartitionsReportar como inadecuado

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1 CES - Centre d-économie de la Sorbonne

Abstract : We consider restricted games on weighted communication graphs associated with minimum partitions. We replace in the classical definition of Myerson-s graph-restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition P min is induced by the deletion of the minimum weight edges. We provide necessary conditions on the graph edge-weights to have inheritance of convexity from the underlying game to the restricted game associated with P min. Then we establish that these conditions are also sufficient for a weaker condition, called F-convexity, obtained by restriction of convexity to connected subsets. Moreover we show that Myerson-s game associated to a given graph G can be obtained as a particular case of the P min-restricted game for a specific weighted graph G ′. Then we prove that G is cycle-complete if and only if a specific condition on adjacent cycles is satisfied on G ′ .

Keywords : restricted game partitions communication networks cooperative game

Autor: Alexandre Skoda -



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