A Theory of Stability in Many-to-Many Matching Markets

By Federico Echenique, Jorge Oviedo. 2004

299 citations recorded by the source corpus.

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one, and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

Subfields: Computational Theory and Mathematics, Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e1ddc7065544661b5de6076c32a1c706b29a55cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Economics and Econometrics

In Management Science and Operations Research

Citations in the corpus

Matching with Couples: Stability and Incentives in Large Markets* (2013, unknown): “…many-to-many matching because each couple may seek two positions.21 Various definitions of stability have been proposed for many-to-many matching, which differ based on the assumptions on what blocking coalitions are allowed (Sotomayor 1999, 2004; Echenique and Oviedo 2006; Konishi and Ünver 18.”
Stability and Competitive Equilibrium in Trading Networks (2013, background): “Sufficiency and necessity of fully substitutable preferences also obtains in settings of many-to-many matching with and without contracts (Roth (1984), Echenique and Oviedo (2006), Klaus and Walzl (2009), and Hatfield and Kominers (2010a) prove sufficiency results; Hatfield and Kojima (2008) and Hat”
Stability in Supply Chain Networks (2005, unknown): “These algorithms are similar to the T -algorithm of Adachi (2000) and Echenique and Oviedo (2004a, 2004b) and the generalized Gale-Shapley algorithm of Hatfield and Milgrom (2005), and all of the above are descendants of the Deferred Acceptance Algorithm (Gale and Shapley, 1962).”