On the existence of population-monotonic solutions on the domain of quasi-convex games

Toru Hokari, Seigo Uchida

Research output: Contribution to journalArticle


On the domain of convex games, the Shapley value and the Dutta–Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.

Original languageEnglish
Pages (from-to)90-92
Number of pages3
JournalOperations Research Letters
Issue number1
Publication statusPublished - 2017 Jan 1



  • Dutta–Ray solution
  • Population-monotonicity
  • Quasi-convex games
  • Shapely value
  • TU-games

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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