Stability of rejections and Stable Many-to-Many Matchings
G. A. Koshevoy ()
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G. A. Koshevoy: CEMI and Poncelet laboratoty (IMU and CNRS (UMI 2615))
No 16-02, Documents de recherche from Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne
For models of many-to-many matchings, stable outcomes exist if agents on both sides have path-independent choice functions. We show that stable outcomes exists if the agents on one side have outcast choice functions and the agents on another have path independent choice functions. All known results on existence of stable outcomes in many-to-many matchings follows from this result. Many-tomany matchings with contracts have stable outcomes under the same conditions. In order to prove our existence theorem, we introduce a new class of telescopic choice functions. We also consider non-symmetric blocking situations and prove that in such a case path-independence can be weakened.
Pages: 12 pages
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