Theoretical Economics, Volume 18, Number 1 ( 2023)

Theoretical Economics 18 (2023), 37–63

Stable matching: an integer programming approach

Chao Huang


This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matching exists in a discrete matching market when firms' preference profile satisfies a unimodularity condition that is compatible with various forms of complementarities. We provide a class of firms' preference profiles that satisfy the unimodularity condition.

Keywords: Two-sided matching, stability, integer programming, many-to-one matching, complementarity, unimodularity, demand type

JEL classification: C61, C78, D47, D63

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