New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalConference article

28 Citations (Scopus)


The concept of M-convex functions plays a central role in "discrete convex analysis", a unified framework of discrete optimization recently developed by Murota and others. This paper gives two new characterizations of M- and M#-convex functions generalizing Gul and Stacchetti's results on the equivalence among the single improvement condition, the gross substitutes condition and the no complementarities condition for set functions (utility functions on {0,1} vectors) as well as Fujishige and Yang's observation on the connection to M-convexity. We also discuss implications of our results in an exchange economy with indivisible goods.

Original languageEnglish
Pages (from-to)495-512
Number of pages18
JournalDiscrete Applied Mathematics
Issue number2
Publication statusPublished - 2003 Sep 12
EventSubmodularity - Atlanta, GA, United States
Duration: 2000 Aug 12000 Aug 1



  • Exchange economy
  • Indivisibility
  • M-convex function
  • M-convex function

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this