## Coincidence of and Linearity Between Game Theoretic Solutions |

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4-person glove game centre characteristic function CIS-vector CIS(v CISi coalition size dependent coalitions with respect convex combination cooperative games core C(v corresponding gap function dependent constant effectiveness condition 3.l efficient payoff vector egalitarian nonseparable contribution ENSC-solution essential coalitions Example 6.l function g game theoretic given by v(N grand coalition gv(N gv(S i e N i,j e imputation set k-coalitional game k-coalitional n-person games l-convexity large coalition left-handed gloves Legros Lemma Let v e Gn main theorem mv(S n_1gv(N n_1NSC(v n-l)-coalitional game n-l)-person coalitions nucleolus pre)-nucleolus concept prekernel prenucleolus Proposition 4.l quota game quota n-person games quota vector real number S C N SCi(v SCj(v segment with end separable contributions set U(v Shapley value single players smallest contributions solution concepts Suppose symmetric symmetric game Theorem 6.9 Toyo University type of games vector q x e I*(v x e U(v Yukihiko Funaki