Existence of Equilibrium in Large Matching Markets With Complementarities

In matching markets, the existence of stable matchings can only be guaranteed under substantive restrictions on preferences. We investigate how these results change in large markets, which we model with a continuum of agents of each type, following the work of Aumann (1964) on general equilibrium theory. We find four main results: First, in many-to-many matching with contracts, stable outcomes do not exist in general. Second, if agents on one side of the market have substitutable preferences, then a stable outcome does exist. Third, with bilateral contracts and transferable utility, competitive equilibria always exist. Fourth, in more general settings with multilateral contracts (possibly including restrictions on transfers) and no structure on the set of agents, the core is nonempty