Existence of Equilibrium in Large Matching Markets With Complementarities

In two-sided matching markets with contracts, the existence of stable outcomes can be guaranteed only under certain restrictions on preferences; the typical restriction is that all agents’ preferences are substitutable. We show that, in markets with a continuum of each type of agent, it is only necessary that agents on one side of the market have substitutable preferences to guarantee the existence of a stable outcome. We also consider more general settings with multilateral contracts and no structure on the set of agents, and show that the core is nonempty when there exists a continuum of agents of each type, regardless of agents’ preferences. Finally, we show that in settings with bilateral contracts and transferable utility (but an arbitrary contractual network), the existence of competitive equilibria is guaranteed regardless of agents’ preferences. We also consider large finite markets, showing that each of the three results above holds approximately in the analogous large finite market.