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

Koji Yokote*, Yukihiko Funaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)171-203
Number of pages33
JournalSocial Choice and Welfare
Volume49
Issue number1
DOIs
Publication statusPublished - 2017 Jun 1

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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