Efficient assignment with interdependent values

We study the “house allocation” problem in which n agents are assigned n objects, one for each agent, when the agents have interdependent values. We show that there exists no mechanism that is Pareto efficient and ex-post incentive compatible, and the only mechanism that is ex-post group incentive compatible is constant across states. By contrast, we demonstrate that a Pareto efficient and Bayesian incentive compatible mechanism exists in the two agent house-allocation problem, given sufficient congruence of preferences and the standard single crossing property. We also show that (approximate) Pareto efficiency can be achieved once we relax the incentive compatibility requirements to approximate ex-post incentive compatibility or Bayesian incentive compatibility.