Convexity of Network Restricted Games Induced by Minimum Partitions

Alexandre Skoda ()
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Alexandre Skoda: Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.univ-paris1.fr

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie 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 Pmin 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 Pmin. 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 Pmin-restricted game for a specific weighted graph G'. Then we prove that G is cycle-complet if and only if a specific condition on adjacent cycles is satisfied on G'

Keywords: Communication networks; cooperative game; restricted game; partitions (search for similar items in EconPapers)
JEL-codes: C6 C61 C7 C71 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2016-03
New Economics Papers: this item is included in nep-gth and nep-mkt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:16019

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