Non-Manipulable House Exchange under (Minimum) Equilibrium Prices

We consider a market with indivisible objects, called houses, and monetary transfers. Each house is initially occupied by one agent and each agent demands exactly one house. The problem is to identify the complete set of direct allocation mechanisms that can be used to reallocate the houses among the agents. On the one hand, for price equilibrium mechanisms, we show that the only strategy-proof mechanism is one with a minimum equilibrium price vector. The result is not true on the classical or the quasi-linear domains, but on reduced domains of preference profiles containing “almost all” profiles in the classical or the quasi-linear domain, respectively. On the other hand, while minimum price equilibrium mechanisms are not necessarily efficient (as prices are not zero), we show that no strategy-proof mechanism Pareto dominates a minimum price equilibrium mechanism, making them constrained efficient in the class of strategy-proof mechanisms.