Credible Group-Stability in General Multi-Partner Matching Problems∗

Pairwise-stable matching mechanisms are practically used and perform very well in the real world two-sided matching markets (e.g., the US hospital-intern market, and the British hospital-intern markets: see Roth 1984 and 1991, respectively). It is known, however, that in a twosided many-to-many matching market (the British market), pairwisestability is not logically related with the (weak) core unlike in a oneto-many matching market (the US market) [see Blair (1988) and Roth and Sotomayor (1990)]. In this paper, we use a graph representation of matching problems, and we define strong group-stability, a matchingvariation of a solution concept in the network literature (Jackson and van den Nouweland, 2002). Although strong group-stability is equivalent to pairwise-stability in a one-to-many matching market, unfortunately, the solution concept is too strong for many-to-many matching markets. Therefore, we proceed to define executable coalitional deviations to discuss the credibility of coalitional deviations, and define credibly group-stable matchings. We prove that credible group-stability is equivalent to pairwise-stability in a wide class of matching problems. We also prove the equivalence between the set of pairwise-stable matchings and the set of matchings resulting from coalition-proof Nash equilibria in an appropriately defined strategic form game. ∗Preliminary. Comments from Al Roth and conversations with Eiichi Miyagawa in the early stage of this research were very useful. †Department of Economics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA 02467, USA. (e-mail): [email protected] (phone): 617-552-1209 (fax): 617-552-2308 ‡Department of Economics, Koç University, Rumeli Feneri Yolu, Sarıyer, 34450 İstanbul, Turkey. (e-mail) [email protected] (phone): (90)-212-338-1354 (fax): (90)-212-338-1653