An axiomatization of the Banzhaf value
type: Item
instance of: scholarly article
title: An axiomatization of the Banzhaf value
zbMATH Open document ID: 0651.90097
DOI: 10.1007/BF01254541
published in: International Journal of Game Theory
publication date: 1988-01-01T00:00:00Z
review text: The Banzhaf value was originally given by an axiomatization. In Owen's book the axiomatization of Banzhaf's value is based on the tool of the compound game and is not determined uniquely. Another axiomatization given by Dubey and Shapley employs a different approach. It is based on four axioms, three of them are standard and in fact determine the semi- value. The author here adopts these three axioms, then replaces the fourth axiom of Dubey and Shapley by some reduction axiom, which has an intuitive meaning. This axiom says something about the value of the game in terms of another game, with a smaller number of players. The author defines for each coalition T two T-games derived from the original game by amalgamating all the players of T to one player called \(\bar T.\) His additional axiom says that for any two-player-coalition \(T=\{i,j\}\) the sum of the values of i and of j in the original game is less or equal to the value of T in the \(\bar T-\)game. According to this axioms a unification of any two players is profitable.
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 4062865
zbMATH Keywords: Banzhaf value
zbMATH Keywords: axiomatization
Wikidata QID: Q29039122
author: Ehud Lehrer
reviewed by: Ezio Marchi
MaRDI profile type: Publication
cites work: On the uniqueness of the Shapley value
cites work: Value Theory Without Efficiency
cites work: Mathematical Properties of the Banzhaf Power Index
cites work: Q3335556
cites work: On the reduced game property and its converse
full work available at URL: https://doi.org/10.1007/bf01254541
OpenAlex ID: W2148579014
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description: scientific article; zbMATH DE number 4062865