A Banzhaf share function for cooperative games in coalition structure

G. van der Laan, J.R. van den Brink

    Research output: Contribution to JournalArticleAcademic

    Abstract

    A cooperative game with transferable utility-or simply a TU-game-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 properties.
    Original languageEnglish
    Pages (from-to)61-86
    Number of pages25
    JournalTheory and Decision
    Volume53
    DOIs
    Publication statusPublished - 2002

    Fingerprint

    Dive into the research topics of 'A Banzhaf share function for cooperative games in coalition structure'. Together they form a unique fingerprint.

    Cite this