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 under responsiveness of agents’ preferences. 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-proo frule 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.