Abstract

It is known that in two-sided many-to-many matching problems, pairwise-stable matchings may not be immune to group deviations, unlike in many-to-one matching problems (Blair, 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise-responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. 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.

Keywords: Many-to-many matching; Pairwise stability; Group stability; Credible deviation; Coalition-proof Nash equilibrium

JEL classification codes: C70; C78; J44

This paper has been circulated under the title “Credible Group Stability in Multi-Partner Matching Problems.” We are most grateful to two anonymous referees of the journal for their exceptionally high-quality services. One referee pointed out an error in one of our results in the first version. The other referee's detailed constructive criticisms led to a completely revised version. Conversations and communications with Al Roth and Federico Echenique were very useful. We thank Bhaskar Dutta, Jordi Massó, Eiichi Miyagawa, William Thomson, Anne van den Nouweland, and the participants of conferences and seminars at BC, Rochester, UBC, Duke, Rice, SMU, Toronto, Brown, Osaka, and Montréal. We also thank Margarita Sapozhnikov for her research assistance. Any errors are our own responsibility. Ünver gratefully acknowledges the support from the NSF.