games. Liability games are superadditive, constant sum, partially convex, and partially concave. The core of a liability … game is empty if and only if the firm is insolvent and has multiple positive liabilities. We analyze the nucleolus of the … game and show that allocating the asset value of the firm using the nucleolus satisfies efficiency, non-negativity, and …

games. Liability games are superadditive, constant sum, partially convex, and partially concave. The core of a liability … game is empty if and only if the firm is insolvent and has multiple positive liabilities. We analyze the nucleolus of the … game and show that allocating the asset value of the firm using the nucleolus satisfies efficiency, non-negativity, and …

-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 …

of players. The social structure is utilized to refine the core of the game. For every coalition the relative strength of … stable core is the set of socially stable elements of the core. We show that the socially stable core is non-empty if the … game itself is socially stable. In general the socially stable core consists of a finite number of faces of the core and …

In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular …