In many real‐life house allocation problems, rents are bounded from above by price ceilings imposed by a government or a local administration. This is known as rent control. Because some price equilibria may be disqualified given such restrictions, this paper proposes an alternative equilibrium concept, called rationing price equilibrium, tailored to capture the specific features of housing markets with rent control. An allocation rule that always selects a rationing price equilibrium is defined, and it is demonstrated to be constrained efficient and (group) non‐manipulable for “almost all” preference profiles. In its bounding cases, the rule reduces to a number of well‐known mechanisms from the matching literature. In this sense, the housing market with rent control investigated in this paper integrates several of the predominant matching models into a more general framework.