Credible group stability in many-to-many matching problems

It is known that in two-sided many-to-many matching problems, pairwisestable 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. Running Title: Credibly Group-Stable Matchings JEL Classification Numbers: C70, C78, J44 ∗This paper has been circulated under the title “Credible Group-Stability under 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. †Department of Economics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA 02467, USA. E-mail: [email protected], phone: +1-617-552-1209, fax: +1-617-552-2308. ‡Department of Economics, Koç University, Rumelifeneri Yolu, Sarıyer, 34450 İstanbul, Turkey. E-mail: [email protected], phone: +90-212-338-1354, fax: +90-212-338-1653.