A two-sided discrete-concave market with possibly bounded side payments: An approach by discrete convex analysis

Satoru Fujishige, Akihisa Tamura

Research output: Contribution to journalArticle

32 Citations (Scopus)


The marriage model due to Gale and Shapley [Gale, D., L. S. Shapley. 1962. College admissions and the stability of marriage. Amer. Math. Monthly 69 9-15] and the assignment model due to Shapley and Shubik [Shapley, L. S., M. Shubik. 1972. The assignment game I: The core. Internat. J. Game Theory 1 111-130] are standard in the theory of two-sided matching markets. We give a common generalization of these models by utilizing discrete-concave functions and considering possibly bounded side payments. We show the existence of a pairwise stable outcome in our model. Our present model is a further natural extension of the model examined in our previous paper [Fujishige, S., A. Tamura. A general two-sided matching market with discrete concave utility functions. Discrete Appl. Math. 154 950-970], and the proof of the existence of a pairwise stable outcome is even simpler than the previous one.

Original languageEnglish
Pages (from-to)136-155
Number of pages20
JournalMathematics of Operations Research
Issue number1
Publication statusPublished - 2007 Feb 1



  • Assignment model
  • Bounded side payments
  • Discrete convex analysis
  • Marriage model
  • Pairwise stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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