Marcin Malawski

Power indices in simple games I : Transfer properties

898

Abstract

The paper contains a review of the most commonly employed power indices of players in simple games and an analysis of their basic properties. We also state and prove two new axiomatizations of the Shapley value as a power index. The Shapley value is the only symmetric index with the null player property and the newly defined "balanced transfer" property, and the index obtained in a natural way from the only additive function with some desirable properties on certain family of sets of coalitions.

Key words: simple game, power index, transfer property, balanced transfer, Shapley value.