Many-to-many matching with max–min preferences

We consider the many-to-many two-sided matching problem under a stringent domain restriction on preferences called the max–min criterion. We show that, even under this restriction, there is no stable mechanism that is weakly Pareto efficient, strategy-proof, or monotonic (i.e., respects improvements) for agents on one side of the market. These results imply in particular that three of the main results of Baïou and Balinski (2000) are incorrect. We also show that one of the results of Baïou and Balinski (2007) is incorrect as well.