Coalitional Exchange Stable Matchings in Marriage and Roommate Markets

We consider the stable roommates problem with respect to the stability based on exchange of agents. We present three natural variants of coalitional exchange stability and identify the relations between them. We also present a number of impossibility results. In particular, we show that even a (standard) exchange stable matching may not exist for dichotomous preferences. We prove that exchange stability has a fundamental incompatibility with weak Pareto optimality. We also prove that an exchange stable matching mechanism cannot be strategyproof.