Credible Group Stability in Multi-Partner Matching Problems

Hideo Konishi and Utku Unver

No 32, Econometric Society 2004 North American Summer Meetings from Econometric Society

Abstract: It is known that in two-sided many-to-many matching markets, pairwise 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 define 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

Keywords: multipartner matching problem; pairwise stability; graph; credible deviations; responsiveness; substitutability (search for similar items in EconPapers)
JEL-codes: C78 (search for similar items in EconPapers)
Date: 2004-08-11
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Related works:
Working Paper: Credible Group Stability in Multi-Partner Matching Problems (2005)
Working Paper: Credible Group Stability in Multi-Partner Matching Problems (2003)
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