Stable matching: an integer programming approach

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.