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-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.We thank the associate editor and the two reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. Both authors acknowledge financial support from Ministerio Economía y Competitividad (Spain) under project ECO2017-87769-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 H2019/HUM-5891. Triossi acknowledges the financial support from the Institute for Research in Market Imperfections and Public Policy, ICM IS130002, Ministerio de Economía, Fomento y Turismo (Chile), and from Ca' Foscari University of Venice under project MAN.INS_TRIOSSI