Abstract
AbstractAsymmetricnetworkconsistsofasetofpositionsandasetofbilaterallinksbetweenthesepositions. Examplesofsuchnetworksareexchangenetworks,com-munication networks, disease transmission networks, control networks etc. Forevery symmetric network we define a cooperative transferable utility game thatmeasuresthe“power”ofeachcoalitionofpositionsinthenetwork. ApplyingtheShapleyvaluetothisgameyieldsanetworkpowermeasure,theβ-measure,whichreflectsthepoweroftheindividualpositionsinthenetwork.Applyingthispowerdistributionmethoditerativelyyieldsalimitdistribution,which turns out to equal the well-known degree measure. We compare the β-measureanddegreemeasurebyprovidingcharacterizations,whichdifferonlyinthenormalizationthatisused.Keywords:symmetricnetworks,networkpower,stationarypowerdistribution,β-measure,degreemeasure.JELcode:C71,Z13. ∗ Correspondingauthor:DepartmentofEconometricsandTinbergenInstitute,FreeUniversity,DeBoelelaan1105,1081HVAmsterdam,TheNetherlands. E-mail: jrbrink@feweb.vu.nl ‡ CentER and Department of Econometrics and Operations Research, Tilburg University, TheNetherlands.
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