Equilibrium and matching under price controls

The paper considers a matching with contracts model in the presence of price controls. The model contains two important streams in the matching literature, those with and those without monetary transfers, as special cases. An adjustment process that ends with a stable outcome is presented. The paper presents a notion of competitive equilibrium, called Drèze equilibrium, and shows Drèze equilibrium allocations to be equivalent to allocations induced by stable outcomes. We therefore have an equivalence that is valid with and without monetary transfers as well as when monetary transfers are limited.