Strategy-proof house allocation with price restrictions

•We consider a house allocation problem with price restrictions.•We investigate a mechanism called the minimal RPE mechanism.•We demonstrate that the mechanism is manipulable in the full preference domain.•We show that the mechanism is strategy-proof in a subset of the full domain.•We demonstrate that this subdomain contains “almost all” preference profiles.

This paper considers a house allocation problem with no initial ownership and where prices are bounded from below and above by exogenously given price restrictions. This type of housing market contains, e.g., the “assignment market” and the “student placement problem” as special cases. A mechanism called the minimal RPE mechanism is defined, and two main results are obtained. First, it is demonstrated that the mechanism is manipulable at some profile in the full preference domain RR. Second, it is proved that there is a subset R˜⊂R of the full domain, containing almost all profiles in RR, such that the minimal RPE mechanism is strategy-proof in that subset.