On the operation of multiple matching markets

We provide a new perspective on how to operate matching markets when there are many types of markets. Our finding is that the market-wise adaptation of strategy-proof and non-wasteful rules yields a strategy-proof rule with the following efficiency property: no strategy-proof rule Pareto-dominates the rule. Such rules are abundant as they include the market-wise use of the well-known priority-based rules of the top trading cycles and the deferred acceptance. This result gives theoretical support to the independent operation of markets observed in real-life markets as well as our practice in Market Design that separately treats each market for its design.