The Blocking Lemma and strategy-proofness in many-to-many matchings

This paper considers the incentive compatibility in many-to-many two-sided matching problems. We first show that the Blocking Lemma holds for many-to-many matchings under the extended max-min preference criterion and quota-saturability condition. This result extends the Blocking Lemma for one-to-one matching and for many-to-one matching to many-to-many matching problem. It is then shown that the deferred acceptance mechanism is strategy-proof for agents on the proposing side under the extended max-min preference criterion and quota-saturability condition. Neither the Blocking Lemma nor the incentive compatibility can be guaranteed if the preference condition is weaker than the extended max-min criterion.