Title: Lipschitz free boundaries in the monopolist's problem

Speaker: Professor Robert McCann, University of Toronto (Canada)

Beijing time: 10: 30-11: 30, May 29th (Wednesday), 2024

Toronto time: 22: 30-23: 30, May 28th (Tuesday), 2024

Zoom Meeting ID: 430 647 4095, Passcode: 202405  

https://us06web.zoom.us/j/4306474095?pwd=neOkgT0fnB41fX5ueNPr7gGvNE2zvE.1&omn=86754488485

Abstract: 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).

报告人简介：Robert McCann现为加拿大多伦多大学国家讲座教授，加拿大皇家科学院院士，2014年国际数学家大会45分钟报告人。主要从事数学物理、偏微分方程、数理经济等领域的理论研究，特别是在最优输运研究领域做出过具有国际影响力的系列研究成果，在Ann. of Math.、JAMS、Invent. Math.、Acta Math.、CPAM、Duke Math. J.、JEMS等国际顶尖数学期刊上发表论文近80篇，现为SIAM J. Math. Anal.、J. Differential Equations、Pure and Applied Analysis等国际数学期刊编委。