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Credible Group Stability in Multi-Partner Matching Problems

  • Utku Unver
  • Hideo Konishi

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.

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Paper provided by Society for Economic Dynamics in its series 2005 Meeting Papers with number 208.

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Date of creation: 2005
Date of revision:
Handle: RePEc:red:sed005:208
Contact details of provider: Postal: Society for Economic Dynamics Marina Azzimonti Department of Economics Stonybrook University 10 Nicolls Road Stonybrook NY 11790 USA
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