Cooperative games in graph structure

摘要: By a cooperative game in coalitional structure or shortly we mean the standard non-transferable utility described by set of payoffs for each coalition that is nonempty subset grand all players.It well-known balancedness sufficient condition nonemptiness core such game.For this result any information on internal organization neglected.In paper generalize concept games and allow organizational within coalitions.For players arbitrarily given structural relation represented graph allowed for.We then consider which possibly empty payoff vectors assigned to every players.Such will be called game.A vector lies if there no group can make its members better off.We define balanced-core as refinement core.To do so, power determined depends relative positions graph.A collection graphs balanced positive weight weighted sum up ones.A it an element sets some graphs.We prove has therefore core.We conclude examples showing usefulness concepts balanced-core.In particular these show close relationship between solutions noncooperative elements well-defined game.This places Nash research program, looking unifying theory approach helps justify clarify other.