Non-atomic fuzzy measures and games
Lyapunov's Theorem for fuzzy measures is proved and it is applied to extend a theorem of \textit{R. J. Aumann} and \textit{L. S. Shapley} [''Values of non-atomic games'' (1974; Zbl 0311.90084)] concerning the existence of the value for non-atomic games. Precisely, it is proved that the range of any non-atomic n-vector fuzzy measure (in the sense of the author [ibid. 10, 135-155 (1983; Zbl 0528.28009)]) is convex and compact and it is shown that this result allows to extend Theorem B from the book cited above (p. 23) from games with unambiguous coalitions to games with fuzzy coalitions (called fuzzy games) defined on \(\sigma\)-algebras of fuzzy sets (which are not necessarily \(\sigma\)-algebras of 'ideal sets').
existence of the value for non-atomic games
scientific article; zbMATH DE number 3936971