Characterization of TU games with stable cores by nested balancedness

A balanced transferable utility game (N, v) has a stable core if its is externally stable, that is, each imputation not in the dominated by some element. Given two payoff allocations x and y, we say outvotes y via coalition S of feasible set dominates allocates at least v(T) to any T contained S. It turns out outvoting transitive M maximal elements with respect coincides only core. By applying duality theorem linear programming twice, it shown certain nested balancedness condition holds. Thus, can be checked finitely many steps whether We super-stable vector less than v(S) element prove super-stability equivalent vital extendability, requiring extendable.