星光直播 星光直播 报告[2025] 126号

(高水平大学建设系列报告1228号)

报告题目：Should a monopolist screen out consumers’ types for maximizing profit?

报告人： 张霜剑 研究员（复旦大学）

报告时间：2025年11月21日下午16:00-17:00

报告地点： 校友广场304会议室

内容摘要：The monoplist 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 1970s. For multidimensional spaces of agents and products, Rochet and Choné (Econometrica, 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 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 moving to the recent progress. The results profoundly connect with the Optimal Transport theory, a powerful tool with potential applications in many areas. This talk contains my joint work with Robert J. McCann and Cale Rankin.

报告人简历：张霜剑，复旦大学星光直播 青年研究员，博士生导师。2018年博士毕业于多伦多大学数学系；博士毕业后曾在巴黎高科国立统计与经济管理星光直播 、巴黎高等师范星光直播 、滑铁卢大学从事博士后研究。2023年9月至今任职于复旦大学星光直播 ，研究方向为最优输运理论在经济金融中的应用，在垄断定价等领域取得重要研究成果。相关研究成果发表在Communications on Pure and Applied Mathematics、Mathematical Models and Methods in Applied Sciences、Advances in Mathematics、Economic Theory、Journal of Mathematical Economics、Conference on Learning Theory等应用数学、经济以及机器学习领域的国际权威期刊和会议上。曾入选国家级高层次青年人才计划。

欢迎师生参加！

邀请人：李婧超

星光直播

2025年11月19日