【题  目】Cooperative Functions

【时  间】2022年5月11日（星期三），14:00-15:30  

【地  点】腾讯会议：349-721-278

【主讲人】曹志刚 教授（北京交通大学经济管理学院）

【主持人】何浩然 教授（北京师范大学经济与工商管理学院）

摘要: The theory of cooperative games is a fundamental branch of game theory and has many applications in economics, management science and computer science. However, the combinatorial nature of the characteristic function (its standard form) and the core (one of its central solution concepts) makes cooperative game theory highly technical to analyze. Four aspects surrounding the core are particularly challenging: (i) closed forms are typically unavailable and proving whether the core is nonempty is technical; (ii) a core is often large when nonempty; (iii) implementing a core allocation often requires the existence of a powerful third-party; (iv) a core allocation may not be robust. This paper makes advances on these fronts by proposing a framework that is based on ordinary functions meeting certain regularity conditions, which are referred to as cooperative functions. Refining the core by solving a class of an infinite number of related problems in a unified way leads to the Walrasian core, a fundamental concept in the general equilibrium theory. We find that the Walrasian core plays a comparable role in the study of cooperative functions as the core does in the study of cooperative games. This framework makes calculus and convex analysis often directly applicable, and closed-form solutions, as well as managerial insights, easier to obtain. Applying this framework to newsvendor games, linear production games and EOQ games easily reproduces several well-known results.

主讲人简介: 曹志刚，北京交通大学经济管理学院教授。主要研究兴趣为博弈论及其应用，包括网络博弈和算法博弈等。在相关领域主流刊物发表论文30余篇，包括Operations Research、Mathematics of Operations Research和Games and Economic Behavior等期刊。