We study strategy-profness in many-to many matching markets.  We prove that when firms have acyclical preferences over workers and both firms and workers have responsive preferences, the worker-optimal stable mechanism is group strategy-proof and Pareto optimal. Absent any assumption on workers’ references, an Adjusted Serial Dictatorship among workers is stable, group strategy-proof and Pareto optimal for workers. In both cases, the set of stable matchings is a singleton. We show that acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets.

Economic Literature Classification Numbers: C71, C78, D71, D78.

Antonio Romero-Medina

Matteo Triossi

Keywords: Acyclicity, Group Strategy-proofness, Many-to-many markets, singleton core., stability