A Banzhaf share function for cooperative games in coalition structure
Theory and Decision 53 (1):61-86 (2002)
Abstract
A cooperative game with transferable utilityâor simply a TU-gameâ describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing propertiesDOI
10.1023/a:1020805106965
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Citations of this work
A model of influence in a social network.Michel Grabisch & Agnieszka Rusinowska - 2010 - Theory and Decision 69 (1):69-96.
References found in this work
Axiomatization of a class of share functions for n-person games.Gerard van Der Laan & René van Den Brink - 1998 - Theory and Decision 44 (2):117-148.