Corpus ID: 232135336

Stable matching: An integer programming approach

@inproceedings{Huang2021StableMA,
  title={Stable matching: An integer programming approach},
  author={Chao Huang},
  year={2021}
}
This paper develops an integer programming approach on two-sided many-to-one matching by investigating stable integral matchings of a fictitious continuum market induced from the original matching market. Each stable integral matching of the continuum market corresponds to a stable matching of the original matching market. We show that a stable matching exists in the original matching market when firms’ preference profile satisfies a unimodularity condition. Our result indicates that a stable… Expand
Unidirectional substitutes and complements
  • Chao Huang
  • Economics
  • 2021
In discrete matching markets, substitutes and complements can be unidirectional between two groups of workers when members of one group are more important or competent than those of the other groupExpand

References

SHOWING 1-10 OF 37 REFERENCES
Job Matching, Coalition Formation, and Gross Substitutes
Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of Shapley and Shubik [7], and of Crawford and KnoerExpand
Existence of Equilibrium in Large Matching Markets With Complementarities
In two-sided matching markets with contracts, the existence of stable outcomes can be guaranteed only under certain restrictions on preferences; the typical restriction is that all agents’Expand
Understanding Preferences: 'Demand Types', and The Existence of Equilibrium with Indivisibilities
We propose new techniques for understanding agents' valuations. Our classification into \demand types", incorporates existing definitions (substitutes, complements, \strong substitutes", etc.) andExpand
Theory of linear and integer programming
  • A. Schrijver
  • Mathematics, Computer Science
  • Wiley-Interscience series in discrete mathematics and optimization
  • 1999
Introduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and LinearExpand
Product-Mix Auctions and Tropical Geometry
TLDR
A new proof of the Unimodularity Theorem is given via the classical unimodularity theorem in integer programming and generalizations of the theorem in higher dimensions are equivalent to various forms of the Oda conjecture in algebraic geometry. Expand
Stable Matching in Large Economies
We study stability of two‐sided many‐to‐one matching in which firms' preferences for workers may exhibit complementarities. Although such preferences are known to jeopardize stability in a finiteExpand
Understanding Preferences: "Demand Types
  • Equilibrium with Indivisibilities. Econometrica
  • 2019
Near-Feasible Stable Matchings with Couples.
TLDR
It is shown that each instance of a matching problem has a "nearby" instance with a stable matching, obtained by perturbing the capacities of the hospitals. Expand
College Admissions and the Stability of Marriage
TLDR
The authors note the college may not know whether the applicant has applied elsewhere and, if so, how she ranked the colleges or whether the other colleges will admit her, so it can likely only admit applicants of a number and quality that are “reasonably close” to their ideal. Expand
Walrasian Equilibrium in Large, Quasilinear Markets
In an economy with indivisible goods, a continuum of agents, and quasilinear utility, we show that equilibrium exists regardless of the nature of agents’ preferences over bundles. This contrasts withExpand
...
1
2
3
4
...