Two-sided strategy-proofness in many-to-many matching markets

We study the existence of group strategy-proof stable rules in many to-many matching markets. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets.Both authors acknowledge financial support from Ministerio Economía y Competitividad (Spain) under project ECO2014 57442 P and from Fondecyt under project No. 1151230. Romero-Medina acknowledges the financial support from Ministerio Economía y Competitividad (Spain) MDM 2014-0431, and Comunidad de Madrid, MadEco-CM (S2015/HUM-3444) and Triossi acknowledges the financial support from the Institute for Research in Market Imperfections and Public Policy, ICM IS130002, Ministerio de Economía, Fomento y Turismo. Triossi acknowledges the hospitality of Collegio Carlo Alberto while writing this paper