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

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

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
Volume131
Issue number2
DOIs
Publication statusPublished - 2003 Sep 12
Externally publishedYes

Fingerprint

Economic Equilibrium
Economic Model
Equilibrium Model
Convex function
Economics
Exchange Economy
Indivisible
Convex Analysis
Discrete Optimization
Complementarity
Substitute
Utility Function
Gross
Convexity
Equivalence

Keywords

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

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities. / Murota, Kazuo; Tamura, Akihisa.

In: Discrete Applied Mathematics, Vol. 131, No. 2, 12.09.2003, p. 495-512.

Research output: Contribution to journalArticle

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