Relationships between the Prenucleolus, ENSC (Egalitarian NonSeparable Contribution) Solution and Related Solution Concepts for Cooperative Games

摘要

The Egalitarian NonSeparable Contribution (ENSC) solution of a cooperative n-person game in characteristic function form is considered. Given that the separable contributions of the single players to the grand coalition are already allocated, the ENSC-method prescribes the egalitarian allocation of the remaining nonseparable contribution in the game. Conditions sufficient for the coincidence of the ENSC-method and the so-called prenucleolus concept are treated. The main result states that both solutions coincide whenever the maximal excesses at the ENSC-solution are determined by the (n-1)-person coalitions in the n-person game. The relationship between the ENSC-method and the so-called Shapley value for a specific type of n-person games is studied. The main result states that the Shapley value of a so-called k-person coalitional game is a linear or convex combination of the ENSC-solution and the center of the set of all nonnegative efficient payoff vectors.