The Controversy of Linearity in Shapley's Axioms

Authors

  • Anton Abdulbasah Kamil

DOI:

https://doi.org/10.11113/matematika.v21.n.521

Abstract

The Shapley value is a unique function which obeys three axioms, which are anonymous, pareto optimal, and linear. This is a solution concept for cooperative games with transferable utility. But when the set of games which is considered is the set of simple games, the condition of linearity has no sense. In this paper, we introduce the concept of monotonicity to answer the controversy in linearity. Keywords: Simple games; power distribution; Shapley value; monotonicity.

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Published

01-12-2005

Issue

Volume 21 (December 2005)

Section

Analysis and Algebra

License

Copyright of articles that appear in MATEMATIKA: MJIAM belongs exclusively to Penerbit UTM Press, Universiti Teknologi Malaysia. This copyright covers the rights to reproduce the article, including reprints, electronic reproductions or any other reproductions of similar nature.

How to Cite

The Controversy of Linearity in Shapley’s Axioms. (2005). MATEMATIKA, 21, 125-131. https://doi.org/10.11113/matematika.v21.n.521