: reduced game monotonicity (RGM) and reduced dominance (RD). Using RGM, RD, NE, Covariance under strategic equivalence, Equal …

-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 …

-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 …

the unique welfare distribution that is core-stable and satisfies the condition that no agent gets a utility payoff above … has an increasing benefit function (no externalities) then every weighted hierarchical solution is core-stable. In case of …

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 …