Monotonicity implies linearity: characterizations of convex combinations of solutions to cooperative games

Koji Yokote*, Yukihiko Funaki

*この研究の対応する著者

研究成果: Article査読

11 被引用数 (Scopus)

抄録

The purpose of this study is to provide a comprehensive characterization of linear solutions to cooperative games by using monotonicity. A monotonicity axiom states an increase in certain parameters of a game as a hypothesis and states an increase in a player’s payoff as a conclusion. We focus on various parameters of a game and introduce new axioms. Combined with previous results, we prove that efficiency, symmetry and a monotonicity axiom characterize (i) four linear solutions in the literature, namely, the Shapley value, the equal division value, the CIS value and the ENSC value, and (ii) a class of solutions obtained by taking a convex combination of the above solutions. Our methodological contribution is to provide a new linear algebraic approach for characterizing solutions by monotonicity. Using a new basis of the linear space of TU games, we identify a class of games in which a solution that satisfies monotonicity is linear. Our approach provides some intuition for why monotonicity implies linearity.

本文言語English
ページ(範囲)171-203
ページ数33
ジャーナルSocial Choice and Welfare
49
1
DOI
出版ステータスPublished - 2017 6 1

ASJC Scopus subject areas

  • 社会科学(その他)
  • 経済学、計量経済学

フィンガープリント

「Monotonicity implies linearity: characterizations of convex combinations of solutions to cooperative games」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル