It is well known since Owen (1968) that the weights in the weighted Shapley value cannot be interpreted as a measure of power (i.e., of the ability to bargain) of the players. This paper proposes a new weight scheme for the Shapley value. Weights in this framework have to be interpreted as a measure of bargaining power. Two different axiomatic characterizations of this new value are proposed: o...

Shapley values, also known as Shapley–Shubik indices, measure the power that agents have in a weighted voting game. Suppose that agent weights are chosen randomly according to some distribution. We show that the expected Shapley values for the smallest and largest agent are independent of the quota for a large range of quotas, and converge exponentially fast to an explicit value depending only ...

The potential approach is a useful tool in physics, and the successful treatment of such concept turned out to be reproducible, in the late eighties, in the field of cooperative game theory. This report is devoted to the modified potential approach for values on cooperative games, particularly for the Shapley value, the Solidarity value, and the class of values satisfying efficiency, linearity ...

This paper provides a flexible strategic framework to analyze bargaining and values in environments with coalitional externalities. Within this framework we propose a new value that extends the Shapley value to partition function form games, the so-called Rational Belief Shapley (RBS) value. We investigate the strategic foundation of the RBS value by constructing an implementation mechanism. Th...

The main contribution of this paper is to give a necessary and sufficient condition under which the Shapley value coincides with the nucleolus, the CIS value and the ENSC value in the following classes of games; airport games (Littlechild and Owen (1973)), bidder collusion games (Graham et al. (1990)) and polluted river games (Ni and Wang (2007)). Along the way, we also show the necessary and s...

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...

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, ...