We study a basic sequential model for the formation of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual decisiveness in simple games, and show that, as for the Shapley-Shubik index, they extend naturally to measures for TU-games. These individual measures, which w...

Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In t...

The “potential approach” to value theory for finite games was introduced by Hart and Mas-Colell (1989). Here this approach is extended to non-atomic games. On appropriate spaces of differentiable games there is a unique potential operator, that generates the Aumann and Shapley (1974) value. As a corollary we obtain the uniqueness of the Aumann-Shapley value on certain subspaces of games. Next, ...

We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote process. We characterize the impact of changing the quota (i.e., the minimum number of seats in the parliament that are required to form a coalition) on the...

This paper defines a class of cooperative fuzzy games with infinite players, which is monotonically nondecreasing and continuous with respect to each player’s grade of membership. Then, the AumannShapley values for the games with fuzzy coalitions are proposed with the form of Choquet integral. The properties of the Aumann-Shapley values are also shown. Finally, the relationship between the fuzz...

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lowervalue based method to associate coalitional games ...

We discuss a subscription game in which service providers (e.g., museums) team up in offering a limited time subscription or access pass allowing unlimited usage of their services. In this game, a natural way to allocate the subscription income among the service providers is by using the Shapley value. We show that, for the particular game considered, the Shapley value takes a very intuitive an...