-convexity, under which the game is shown to have a non-empty core and the average tree solution lies in the core. In general, link …

of ones. We then define the balanced-core as a refinement ofthe core. A payoff vector lies in the balanced-core if it … lies in the core andthe payoff vector is an element of payoff sets of all graphs in some balanced collection ofgraphs. We … prove that any balanced graph game has a nonempty balanced-core.We conclude by some examples showing the usefulness of the …