the core andthe payoff vector is an element of payoff sets of all graphs in some balanced collection ofgraphs. We prove … determinedthat depends on the relative positions of the players within the graph.A collection of graphs will be called balanced if to … ones. We then define the balanced-core as a refinement ofthe core. A payoff vector lies in the balanced-core if it lies in …

that although the game is not convex its core is always non-empty. Furthermore we provide a painting algorithm for large …