Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/118142
Authors: 
Konishi, Hideo
Ünver, M. Utku
Year of Publication: 
2003
Series/Report no.: 
Nota di Lavoro, Fondazione Eni Enrico Mattei 115.2003
Abstract: 
It is known that in two-sided many-to-many matching markets, pair-wise stability is not logically related with the (weak) core, unlike in many-to-one matching markets (Blair, 1988). In this paper, we seek a theoretical foundation for pairwise stability when group deviations are allowed. Group deviations are defined in graphs on the set of agents. We introduce executable group deviations in order to discuss the credibility of group deviations and to defined credibly group stable matchings. We show, under responsive preferences, that credible group stability is equivalent to pairwise stability in the multi-partner matching problem that includes two-sided matching problems as special cases. Under the same preference restriction, we also show the equivalence between the set of pairwise stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic form game. However, under a weaker preference restriction, substitutability, these equivalences no longer hold, since pairwise stable matchings may be strictly Pareto-ordered, unlike under responsiveness.
Subjects: 
Multi-partner matching problem
Pairwise stable matching network
Credible group deviation
JEL: 
C71
C72
C78
J41
Document Type: 
Working Paper

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