House Allocation with Overlapping Agents: A Dynamic Mechanism Design Approach

Many real-life applications of house allocation problems are dynamic. For example, in the case of on-campus housing for college students, each year freshmen apply to move in and graduating seniors leave. Each student stays on campus for a few years only. A student is a “newcomer” in the beginning and then becomes an “existing tenant.” Motivated by this observation, we introduce a model of house allocation with overlapping agents. In terms of dynamic mechanism design, we examine two representative static mechanisms of serial dictatorship (SD) and top trading cycles (TTC), both of which are based on an ordering of agents and give an agent with higher order an opportunity to obtain a better house. We show that for SD mechanisms, the ordering that favors existing tenants is better than the one that favors newcomers in terms of Pareto efficiency. Meanwhile, this result holds for TTC mechanisms under time-invariant preferences in terms of Pareto efficiency and strategy-proofness. We provide another simple dynamic mechanism that is strategy-proof and Pareto efficient.