The Enemy of My Enemy Is My Friend: A New Condition for Two-sided Matching with Complementarities

Stable matchings in the presence of complementarities need not exist. With a canonical form of payoff functions, the conventional sufficient condition for existence substantially restricts the range of pairwise complementarity/substitutability values. This paper provides a new sufficient condition for existence on the maximal range of complementarities/substitutabilities. Our condition also allows for a new class of settings that are relevant to labor markets but violate the conventional condition. We further show that under a minor assumption, our condition is also necessary to guarantee existence. Note that the preferences in our model are not captured by Baldwin and Klemperer (forthcoming).