Stability and Generalized Competitive Equilibria in a Many-to-Many Gale-Shapley Market Model
Stability and Generalized Competitive Equilibria in a Many-to-Many Gale-Shapley Market Model

Summary/Abstract: We define, for some variant of a many-to-many market model of Gale-Shapley type, a concept of generalized competitive equilibrium and show that, under suitable conditions, stable matchings in such a model can be represented as competitive equilibria allocations (and vice versa). Our results are far-reaching generalizations of the “discrete supply and demand lemma” of Azevedo, Leshno (2011) for the college admissions market. Using the results of Alkan, Gale (2003), we also prove a theorem on existence of generalized equilibria in our model.

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