Manipulability in matching markets: conflict and coincidence of interests

We study comparative statics of manipulations by women in the men-proposing deferred acceptance mechanism in the two-sided one-to-one marriage market. We prove that if a group of women weakly successfully manipulates or employs truncation strategies, then all other women weakly benefit and all men are weakly harmed. We show that these results do not appropriately generalize to the many-to-one college admissions model.