Convexity of Network Restricted Games Induced by Minimum Partitions

Alexandre Skoda ()
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Alexandre Skoda: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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 (search for similar items in EconPapers)
Date: 2016-03
New Economics Papers: this item is included in nep-gth
Note: View the original document on HAL open archive server: https://hal.science/hal-01305005v1
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Citations: View citations in EconPapers (17)

Published in 2016

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