Academic Report of School of Mathematical Sciences [2025] No. 126

(Series Report for High-Level University Construction No. 1228)

Title: Should a monopolist screen out consumers' types for maximizing profit?

Speaker: Researcher Zhang Shuangjian (Fudan University)

Time: 16:00-17:00, November 21, 2025 (Friday)

Location: Alumni Square, Room 304

Abstract:

The monopolist problem is one of the central problems in microeconomics with many applications. Existence, uniqueness, convexity/concavity, regularity, and characterization of the solutions have been widely studied since the 1970s. For multidimensional spaces of agents and products, Rochet and Choné (Econometrica, 1998) reformulated this problem as a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a quasilinear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem. This duality allows us to reduce the solution of the square example of Rochet-Choné to a novel free boundary problem, giving the first analytical description of an overlooked market segment, where the regularity built by Caffarelli-Lions plays a crucial role —— an extension of their regularity work to the quasilinear case is also recently studied. In this talk, I will first introduce the historical work on the principal-agent framework under the context of the monopolist problem before discussing recent progress. The results are profoundly connected with Optimal Transport theory, a powerful tool with potential applications in many areas. This talk is based on my joint work with Robert J. McCann and Cale Rankin.

Speaker Biography:

Zhang Shuangjian is a Young Investigator and Doctoral Supervisor at the School of Mathematical Sciences, Fudan University. He received his Ph.D. from the Department of Mathematics at the University of Toronto in 2018. After his Ph.D., he conducted postdoctoral research at the École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris), the École Normale Supérieure (Paris), and the University of Waterloo. He joined the School of Mathematical Sciences at Fudan University in September 2023. His research focuses on the application of optimal transport theory in economics and finance, where he has achieved significant results in areas such as monopoly pricing. His related research has been published in leading international journals and conferences in applied mathematics, economics, and machine learning, including Communications on Pure and Applied Mathematics, Mathematical Models and Methods in Applied Sciences, Advances in Mathematics, Economic Theory, Journal of Mathematical Economics, and the Conference on Learning Theory. He has been selected for the National-level Young Talents Program.

All faculty and students are welcome!

Host: Li Jingchao

School of Mathematical Sciences

November 19, 2025