Values of nondifferentiable vector measure games (Q378326)

The Shapley value, introduced as a solution concept for cooperative games with finitely many players, has been successfully extended to differentiable non-atomic games [\textit{R. J. Aumann} and \textit{L. S. Shapley}, Values of non-atomic games. Princeton, N. J.: Princeton University Press (1974; Zbl 0311.90084)]. \textit{J. F. Mertens} [Int. J. Game Theory 17, No. 1, 1--65 (1988; Zbl 0663.90102)] showed that there exists a unique value function on a much larger space containing non-differentiable games. Moreover, for the space spanned by games that are functions of finitely many measures, \textit{A. Neyman} [Isr. J. Math. 124, 1--27 (2001; Zbl 1027.91004)] constructed a value that may depend on the employed Banach limit. Using methods from distribution theory, by developing suitable diagonal formulas, the author shows that for each game in the intersection of both extended spaces, for which the Banach limit is the usual limit, the value concepts of Mertens and Neyman coincide. This result may be considered as a step towards a characterization of value functions on domains of vector measure games with bounded variation, a problem already mentioned by Neyman.