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

Hideto Koizumi, Hitotsubashi University

Abstract: 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).

Read the full working paper here (PDF).