Complementarity and Multidimensional Heterogeneity in Matching Markets

It is well-known that in two-sided matching markets (with contracts) that the existence of a stable outcome can be guaranteed if and only if agents’ preferences are substitutable and contracts are bilateral. 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 in order to guarantee the existence of a stable outcome. We also consider more general economies 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 no structure on the set of agents), 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. JEL Classification: C62, C78, D4, D86, D86, L14