Strategy-Proof House Allocation with Price Restrictions

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. Second, it is proved that there is a subset of the full domain, containing almost all profiles in the full domain, such that the minimal RPE mechanism is strategy-proof in that subset.