Housing Markets with Endogenous Budget Constraints∗

This paper addresses the existence of competitive equilibrium in the variant of the Assignment Game where budget-constrained agents are endowed with one good, that can be sold to buy another good. We define the Money Scarcity (MS) condition and its Strong (SMS) and Weak (WMS) versions. The WMS condition ensures the existence of an equilibrium in cases where Quinzii’s indispensability of money assumption does not hold. We consider two mechanisms to find a competitive equilibrium which are extended versions of Gale’s Top Trading Cycles algorithm and of the Exact Auction Mechanism of Demange, Gale and Sotomayor. Under MS, the first mechanism is strategy-proof; the second is not. We strengthen the MS condition (SMS) to guarantee the existence of Nash equilibria in the revelation game induced by the second mechanism, where the outcome coincides with the assignment found by the first mechanism; moreover, this assignment is Pareto efficient.