简介
理悦CEMA•璇玑系列讲座第二讲将于2026年4月21日（周二）及2026年4月23日（星期四）下午15：30-17：00在学术会堂712会议室举行，由约翰·霍普金斯大学的Abram Hutzler政治经济学教授M. Ali Khan报告以下内容：
Talk 1:Continuity postulates and solvability axioms in economic theory and in mathematical psychology: A consolidation of the theory of individual choice.
Talk 2:Separately Convex and Separately Continuous Preferences: Axioms for Cardinal and Ordinal Utility in n-Person Games
欢迎广大师生（尤其是对科研有兴趣和追求的本科生、硕士生和博士生）参加。讲座对所有人免费开放，不需要提前预约。
题目
Talk 1: Continuity postulates and solvability axioms in economic theory and in mathematical psychology:
A consolidation of the theory of individual choice.
（经济理论与数学心理学中的连续性公设与可解性公理：对个人选择理论的整合）
Talk 2: Separately Convex and Separately Continuous Preferences: Axioms for Cardinal and Ordinal Utility in n-Person Games
（单凸与单连续偏好：n人博弈中基数效用与序数效用的公理）
报告人
M. Ali Khan
M. Ali Khan is Abram Hutzler Professor of Political Economy at Johns Hopkins University. His broad research interests include mathematical economics, general equilibrium, large economy and large games. His research has appeared in leading economics and mathematics journals, including Econometrica, Review of Economic Studies, Quarterly Journal of Economics, Journal of Economic Theory ,Theoretical Economics, Economic Theory , International Economic Review, Journal of International Economics, Journal of Mathematical Economics, Journal of Public Economics, Transactions of the American Mathematical Society, Advances in Mathematics.
摘要
Talk1: On taking the intermediate value theorem (IVT) and its converse as a point of departure, this talk connects the intermediate value property (IVP) to the continuity postulate typically assumed in mathematical economics, and to the solvability axiom typically assumed in mathematical psychology. This connection takes the form of four portmanteau theorems, two for functions and the other two for binary relations, that give a synthetic and novel overview of the subject. In supplementation, the talk will also surveys the antecedent literature both on the IVT itself, as well as its applications. in economic and decision theory. The work underscores how a humble theorem, when viewed in a broad historical frame, bears the weight of many far-reaching consequences; and testifies to a point of view that the apparently complicated can sometimes be under-girded by a most basic and simple execution.
讲座1:本报告以介值定理及其逆定理为起点，将介值性质与数理经济学中常用的连续性假设、数学心理学中常用的可解性公理建立联系。这一联系通过四个综合性定理展开，其中两个针对函数，另外两个针对二元关系，为相关研究提供了整合性的全新梳理。报告还回顾了介值定理及其在经济与决策理论中应用的已有文献。研究表明，一个看似简单的定理，在更宽广的学术脉络中能够引申出诸多重要结论；也体现出，看似复杂的问题，往往可以由最基础、简洁的逻辑加以支撑。
Talk2: The fact that a function of several variables may satisfy a property for one variable and not necessarily for any other has been understood and appreciated in economic theory at least since Debreu's 1952 reformulation of Nash's theorem as a 'social existence theorem.' This talk provides a systematic investigation of this kind of separate convexity property for preferences and correspondences, and explores its interplay with the continuity postulate. We present three equivalence theorems on preferences, and apply them to obtain representations of both cardinal and ordinal utilities in the formulation of n-person games. Moreover, we provide characterizations of the open graph property for correspondences with separately convex sections that substantially generalize the results of Bergstrom-Parks-Rader, Schmeidler, and Shafer on the continuity of correspondences.
讲座2:经济学界早已认识到，多元函数可能仅对单个变量满足某种性质，而对其他变量不一定满足，这一认识至少可追溯至德布鲁1952年将纳什定理改写为“社会存在性定理”的工作。本报告对偏好与对应关系的单凸性质进行系统分析，并探讨它与连续性假设之间的关系。报告给出三个关于偏好的等价定理，并将其用于刻画N人博弈中的基数效用与序数效用表达。同时，报告对具有单凸截面的对应关系的开图性质进行刻画，进一步拓展了伯格斯特伦、帕克斯、雷德、施迈德勒、谢弗等学者关于对应关系连续性的相关结论。
时间
Talk1:4月21日（星期二）15:30-17:00
Talk2:4月23日（星期四）15:30-17:00
地点
学术会堂712
活动对象
创新发展学院师生
主办单位
创新发展学院
中国经济与管理研究院
撰稿：M. Ali Khan
审稿：何其春
编辑：沈嘉怡
审核：赵扶扬
