Distinguished Lecture——Lipschitz free boundaries in the monopolist's problem
报告人：Robert McCann (University of Toronto)
时间：2024-05-31 13:30-14:30
地点：智华楼四元厅
摘要：The principal-agent problem is an important paradigm in economic theory for studying the value of private information; the nonlinear pricing problem faced by a monopolist is one example; others include optimal taxation and auction design. For multidimensional spaces of consumers (i.e. agents) and products, Rochet and Chone (1998) reformulated this problem to a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a (quasi)linear sensitivity to prices. This optimization corresponds mathematically to a convexity-constrained obstacle problem.
The solution is divided into multiple regions, according to the rank of the Hessian of the optimizer. We show the free boundary separating the highest rank regions to be locally Lipschitz. Combining our techniques with those of Rochet and Chone allows us to confirm conjectured aspects of the solution to their square example, and gives the first analytical description of an overlooked market segment.
Based on work-in-progress with Cale Rankin (University of Toronto) and Kelvin Shuangjian Zhang (Fudan University).
个人简介：Robert John McCann received his PhD in mathematics from Princeton University in 1994. He was a Tamarkin Assistant Professor at Brown University from 1994, before joining the University of Toronto Department of Mathematics in the fall of 1998. He has worked as a professor at the University of Toronto since 1998, and as Canada Research Chair in Mathematics, Economics, and Physics since 2020. McCann was an invited speaker at the International Congress of Mathematicians in Seoul in 2014. He was elected a Fellow of the American Mathematical Society in 2012, of the Royal Society of Canada in 2014, of the Fields Institute in 2015 and of the Canadian Mathematical Society in 2020. He is known for his work in transportation theory. He invented the displacement interpolation between probability measures and studied the convexity of various entropies and energies along it, later linking these to Ricci curvature and eventually to the Einstein equations of general relativity. He has pioneered applications of optimal transport to economic problems such as hedonic matching, investment to match, and multidimensional screening.
