I. Ekeland
Pacific Institute for the Mathematical Sciences, Vancouver

Optimal Transportation, Matching Problems, and Economic Equilibrium

Abstract: The optimal transportation problem consists of finding a measure-preserving map between two sets which maximizes some integral criterion. We apply the methods of optimal transportation to solve various problems arising in economic theory, and notably to find equilibria in markets for quality goods. These are goods like cars, houses, or jobs - the issue is not how many you have, but whether you have one and how good it is if you have one. We prove that, under suitable assumption, there exist a unique price that will clear the market for every quality. If time permits, we will also give some extensions to multi-person matching problems.