Application of M-Convex submodular flow problem to mathematical economics

Kazuo Murota, Akihisa Tamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

This paper shows an application of the M-convexs ubmodular flow problem to an economic model in which producers and consumers trade various indivisible commodities through a perfectly divisible commodity, money. We give an efficient algorithm to decide whether a competitive equilibrium exists or not, when cost functions of the producers are M« convex and utility functions of the consumers are M« concave and quasilinear in money. The algorithm consists of two phases: the first phase computes productions and consumptions in an equilibrium by solving an M-convexs ubmodular flow problem and the second finds an equilibrium price vector by solving a shortest path problem.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages14-25
Number of pages12
Volume2223 LNCS
DOIs
Publication statusPublished - 2001
Externally publishedYes
Event12th International Symposium on Algorithms and Computation, ISAAC 2001 - Christchurch, New Zealand
Duration: 2001 Dec 192001 Dec 21

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2223 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other12th International Symposium on Algorithms and Computation, ISAAC 2001
CountryNew Zealand
CityChristchurch
Period01/12/1901/12/21

Fingerprint

Economics
Competitive Equilibrium
Indivisible
Economic Model
Shortest Path Problem
Divisible
Utility Function
Cost functions
Convex function
Cost Function
Efficient Algorithms
Money

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Murota, K., & Tamura, A. (2001). Application of M-Convex submodular flow problem to mathematical economics. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2223 LNCS, pp. 14-25). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2223 LNCS). https://doi.org/10.1007/3-540-45678-3_2

Application of M-Convex submodular flow problem to mathematical economics. / Murota, Kazuo; Tamura, Akihisa.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2223 LNCS 2001. p. 14-25 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2223 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Murota, K & Tamura, A 2001, Application of M-Convex submodular flow problem to mathematical economics. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 2223 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2223 LNCS, pp. 14-25, 12th International Symposium on Algorithms and Computation, ISAAC 2001, Christchurch, New Zealand, 01/12/19. https://doi.org/10.1007/3-540-45678-3_2
Murota K, Tamura A. Application of M-Convex submodular flow problem to mathematical economics. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2223 LNCS. 2001. p. 14-25. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45678-3_2
Murota, Kazuo ; Tamura, Akihisa. / Application of M-Convex submodular flow problem to mathematical economics. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2223 LNCS 2001. pp. 14-25 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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