Respect for Improvements and Comparative Statics in Matching Markets

One of the oldest results in the theory of two-sided matching is the entry comparative static, which shows that under the Gale-Shapley deferred acceptance algorithm, adding a new agent to one side of the market makes all the agents on the other side weakly better off. Here, we give a new proof of the entry comparative static, by way of a well-known property of deferred acceptance called respect for improvements. Our argument extends to yield comparative static results in more general settings, such as matching with slot-specific preferences.