Non-Manipulable House Exchange under (Minimum) Equilibrium Prices

We consider a market with indivisible objects, called houses, and money. On this market, each house is initially owned (or rented) by some agent and each agent demands precisely 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. The focus is on price mechanisms, i.e., mappings of preference profiles to price equilibria, that are strategy-proof and satisfy an individual rationality condition. We prove that the only mechanism that satisfies these conditions is a price mechanism with a minimal equilibrium price vector. The result is not true in full preference domain. Instead, we identify a smaller domain, that contains almost all profiles, where the result holds.