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

• Authors: Zbigniew Świtalski

Title variants

PL

Stabilność i uogólnione równowagi konkurencyjne w modelu rynku Gale’a-Shapleya typu „many-to-many”

Abstracts

PL

W artykule zdefiniowano, dla pewnego wariantu modelu rynku Gale’a-Shapleya (typu „many-to-many”), pojęcie uogólnionej równowagi konkurencyjnej i pokazano, że przy odpowiednich założeniach, skojarzenia stabilne w tym modelu mogą być reprezentowane jako alokacje równowag konkurencyjnych (i vice versa). Przedstawione wyniki są daleko idącymi uogólnieniami „lematu o podaży i popycie” z pracy Azevedo, Leshno (2011) dotyczącego modelu rekrutacji kandydatów do szkół. Wykorzystując wyniki Alkana, Gale’a (2003), udowodniono również twierdzenie o istnieniu uogólnionych równowag dla podanego modelu.

EN

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.

Keywords

EN

stable matching; Gale-Shapley theory; many-to-many model; competitive equilibrium; discrete market model; contract theory

PL

kojarzenie stabilne; teoria Gale-a-Shapleya; model „many-to-many”; równowaga konkurencyjna; dyskretny model rynku; teoria kontraktów

• Publisher: Główny Urząd Statystyczny
• Journal: Przegląd Statystyczny
• Year: 2016
• Volume: 63
• Issue: 3
• Pages: 237-254

Dates

published

2016

Contributors

author

Zbigniew Świtalski

References

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Identifiers

Biblioteka Nauki

1050555