Summary
The first part is the study of several conditions which are sufficient for the coincidence of the prenucleolus concept and the egalitarian nonseparable contribution (ENSC-) method. The main sufficient condition for the coincidence involved requires that the maximal excesses at the ENSC-solution are determined by the (n-1)-person coalitions in then-person game. The second part is the study of both a new type of games, the so-calledk-coalitionaln-person games, and the interrelationship between solutions on the class of those games. The main results state that the Shapley value of ak-coalitionaln-person game can be written as a convex or affine combination of the ENSC-solution and the centre of the imputation set.
Zusammenfassung
Im ersten Teil der Arbeit werden verschiedene hinreichende Bedingungen für die Koinzidenz des Prenukleolus-Lösungskonzepts und der ENSC-Regel vorgestellt. Es wird dabei gezeigt, daß der Prenukleolus mit der ENSC-Lösung zusammenfällt, falls die maximalen Exzesse der ENSC-Lösung durch die (n-1)-Personen Koalitionen desn-Personenspiels bestimmt werden. Im zweiten Teil der Arbeit untersuchen wir eine Klasse von Spielen, die sogenanntenk-Koalitions-n-Personenspiele und untersuchen die Zusammenhänge zwischen den Lösungskonzepten für diesen speziellen Typ von Spielen. Es stellt sich heraus, daß der Shapleywert einesk-Koalitions-n-Personenspiels beschrieben werden kann als eine Linearkombination der ENSC-Lösung und des Schwerpunktes der Auszahlungsmenge.
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Driessen, T.S.H., Funaki, Y. Coincidence of and collinearity between game theoretic solutions. OR Spektrum 13, 15–30 (1991). https://doi.org/10.1007/BF01719767
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DOI: https://doi.org/10.1007/BF01719767