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 is a revised version of TI-discussion paper 8-95-249, \ An axiomatization of the Shapley value using component eeciency and fairness". I would like to thank Gerard van der Laan and Eric van Damme for useful remarks on a previous draft of this paper. Financial support from the Netherlands organization for scientiic research (NWO) ESR-grant 510-01-0504 is gratefully acknowledged. Abstr...

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...

Cost allocation problems arise in many contexts in economics and management science. In a typical problem that we have in mind, a decision maker must decide how to allocate the joint cost of production among several commodities using prices. Furthermore, these prices must satisfy certain reasonable postulates among which is the requirement that total revenue associated with these prices must co...

The Shapley value, one of the most widespread concepts in Operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. Recently much research work has been done in order to extend OR models and methods, in particular cooperative game theory, for situations with interval data. This paper focuses on the Shapley value ...

We provide several new characterizations of well known cost sharing methods (CSMs) as maxima of linear (or convex) functionals. For the Shapley-Shubik method the characterization has an interpretation in terms of randomly ordered agents choosing their most preferred CSM, while the characterizations of the Aumann-Shapley and Serial methods have a very general character: any symmetric convex func...

We study 4 × 4 games for which the best response dynamics contain a cycle. We give examples in which multiple Shapley polygons occur for these kinds of games. We derive conditions under which Shapley polygons exist and conditions for the stability of these polygons. It turns out that there is a very strong connection between the stability of heteroclinic cycles for the replicator equation and S...