Population monotonic allocation schemes for games with externalities

Takaaki Abe*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This paper provides conditions for a game with externalities to have a population monotonic allocation scheme (PMAS). We observe that the notion of convexity defined by Hafalir [Games Econ Behav 61:242–258, 2007] does not guarantee the existence of a PMAS in the presence of externalities. We introduce a new notion of convexity and show that while our convexity is not a stronger condition than Hafalir’s [Games Econ Behav 61:242–258, 2007] , it is a sufficient condition for a game to have a PMAS. Moreover, we show that the Aumann-Drèze value, which is defined for games with coalition structures, explicitly constructs a PMAS. In addition, we offer two necessary and sufficient conditions to guarantee a PMAS in the presence of externalities.

Original languageEnglish
Pages (from-to)97-117
Number of pages21
JournalInternational Journal of Game Theory
Issue number1
Publication statusPublished - 2020 Mar 1


  • Convexity
  • Core
  • Externalities
  • Population monotonicity

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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