The article explores how matching between two parties can be stable even with price controls in place. The researchers show that a process involving a specific algorithm can lead to a stable outcome. They introduce a new concept called Drèze equilibrium, which is a type of competitive balance in this scenario. The study proves that Drèze equilibrium allocations are the same as stable outcomes, indicating the existence of such equilibria. This finding suggests that competitive balance and stable outcomes are equivalent, even when monetary transfers are involved or restricted.