For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept. Convexity can be defined in a number of ways, each having its own specific attractions. Basically, these definitions fall into two categories, namely those based on a...

The notion of automorphism is an essential tool to capture the meaning of any mathematical structure. We apply this idea to cooperative games and obtain two interesting characterizations of the automorphisms of such a game: the one, in the complete case, as the permutations of players which...

We consider situations in which shares of n firms are held by the same n firms as well as by individual investors. The problem is to determine the actual control of the firms by the individual investors. In part 1, we develop the mathematical model, and explain the basic notions of clutter and...

The space of continuous, piecewise smooth homogeneous functions of degree one in two variables can be generated by linear functions and by functions which are the minimum of two linear expressions. This permits a representation of the value for homogeneous games on two measures in terms of the...

In this paper we provide an axiomatization of the Shapley value for TU-games using a fairness property. This property states that if to a game we add another game in which two players are symmetric then their payoffs change by the same amount. We show that the Shapley value is characterized by...