Sequential Rules for House Allocation with Price Restrictions

This paper considers a housing market with price restrictions. On such market, price equilibrium may be excluded for certain preference profiles. However, the existence of a unique minimal rationing price equilibrium has previously been established on a general preference domain that contains "almost all" preference profiles. This type of equilibrium has been demonstrated to be an important ingredient in a direct and strategy-proof allocation mechanism for housing markets with price restrictions. The main contribution of this paper is to provide a finite ascending price sequence that terminates to a minimal rationing price equilibrium. This sequence is demonstrated to play a key-role in an Iterative English Auction Rule for housing markets with price restrictions.