Paper Large Matching Markets

Large matching models allow for a simpler description of matching markets. In physics, models of a handful of molecules are complicated, but it is simple to characterize the behavior of a gas consisting of great numbers of molecules moving in all directions. Likewise, by considering continuum models or the limit of increasingly large markets we are able to tractably characterize the main features of the market and to abstract away from discreteness constraints or pathological situations. The analytic tractability of large matching models allows us to ask a richer set of questions. To motivate the discussion, this chapter focuses on one such vein of questions: does the choice of the proposing side in the DA algorithm matter? If it does, how much does it matter? These questions pose a long-standing puzzle. In it was shown that men receive their optimal matching in the men-proposing DA but their pessimal matching. 

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