Incentive compatibility and feasibility constraints in housing markets

We analyze centralized housing markets under the existence of feasibility constraints on the number of agents and objects involved in the exchanges. We focus on an incomplete information setting where only the information about how each agent ranks her endowment is private. We show that under non-degenerate ex-ante probability distributions over preference profiles, no rule satisfies the joint requirements of individual rationality, (constrained) efficiency, and ordinally Bayesian incentive compatibility.