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Superadditivity for solutions of coalitional games. (English) Zbl 0684.90105
Summary: It is well-known that the Shapley value is an additive and even linear solution concept. We describe a suitable basis for the null space of the Shapley value and give an algorithm to compute the Shapley value in a surveyable manner. The core is known to be a superadditive solution. We prove that it is additive for convex games. In terms of a new concept - maximal tightly balanced collection - we describe the dimension of the core and cones of games where the least core is superadditive.

91A12 Cooperative games