Abstract
We analyze many to one matching problems in the presence of external effects. We extend the notion of '-stability (Sasaki and Toda (1996), Two sided matching problems with externalities, Journal of Economic Theory, 70, 93-108) based on the concept of estimation functions '. We show that the set of '-stable matchings may be empty for some instances of the many to one problem. Further, even under full admissibility, i.e. a situation where each matching is admissible for all agents, the non-existence of '-stable matchings remains. Hence, we provide a condition on …rms’preferences, called bottom substitutability, that guarantees the existence of at least one '-stable matching under full admissibility. Under the assumption that agents are pessimistic enough, we provide a set of pessimistic estimation functions, which depends on agents’preferences and implies that full admissibility is neither necesary nor su¢ cient for the general existence of '-stable matchings. In addition, we show that for any problem, a notion of the core with non-myopic agents ('-core) and the set of '-stable matchings always coincide given any set of estimation functions '. JEL classi…cation numbers: C78, D62, D81.
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