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...

In this paper we consider a proper Shapley value (the V L value) for cooperative network games. This value turns out to have a nice interpretation. We compute the V L value for various kinds of networks and relate this value to optimal strategies in an associated matrix game

If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of...

In this paper we introduce three-valued simple games as a natural extension<br/>of simple games. While simple games are used to evaluate single voting systems, three-valued simple games offer the opportunity for a simultaneous analysis of two different voting systems within the same parliamentary...

Abstract: This paper introduces a new class of interactive cooperative purchasing situations and provides an explicit alternative characterization of the nucleolus of cooperative games, which offers an alternative to Kohlberg (1971). In our cooperative purchasing situation, the unit price of a...