We introduce ideas and methods from distribution theory into value theory. This new approach enables us to construct new diagonal formulas for the Mertens value (Int J Game Theory 17:1–65, <CitationRef CitationID="CR5">1988</CitationRef>) and the Neyman value (Isr J Math 124:1–27, <CitationRef CitationID="CR6">2001</CitationRef>) on a large space of non-differentiable games....</citationref></citationref>

In Kleinberg and Weiss, Math Soc Sci 12:21–30 (<CitationRef CitationID="CR14">1986b</CitationRef>), the authors used the representation theory of the symmetric groups to characterize the space of linear and symmetric values. We call such values “membership” values, as a player’s payoff depends on the worths of the coalitions to...</citationref>

We will find 3 maximal subclasses with respect to essential, superadditive and convex games, respectively such that a game is in one subclass, so are its reduced games.

Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows...

A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. We study the extended Shapley value as proposed by Derks and Peters (1993). Van den Nouweland (1993) provided a characterization that is an extension of Young's (1985) characterization...