管理科学与工程上海市高水平大学建设学科报告（六）

报告题目：Walrasian PMAS

报告人：曹志刚教授

工作单位：北京交通大学

时间：2022年11月15日（周二）晚上7:00-9:00

腾讯会议号：630-882-512

报告摘要

Refining the core and being more easily implemented in a dynamic way, PMAS (Population Monotonic Allocation Scheme) is an important solution concept in the theory of cooperative games. Yet verifying whether a cooperative game is PMAS-admissible is nontrivial. For a large class of cooperative games referred to as superadditive market games (SMG), we propose several new solution concepts that further refine the PMAS.  Each SMG is characterized by a set of players, their initial endowments, and a superadditive function referred to as a cooperative function.  Our solution concepts can be more easily handled by directly studying the underlying cooperative functions (which are continuous instead of discrete).  Each SMG could be viewed as an exchange economy and the set of Walrasian equilibrium price vectors, referred to as the Walrasian core, could be used to refine the core. We define Walrasian PMAS by imposing certain monotonicity requirements on Walrasian core price vectors, as imposed on the core allocations in the definition of PMAS. We call a cooperative function that always derive PMAS-admissible SMGs PMAS kind. We prove that a cooperative function is PMAS kind if and only if its Walrasian PMAS is nonempty,  and that a cooperative game is PMAS-admissible if and only if it can be represented as an SMG with a PMAS kind cooperative function.   Ultramodular functions (functions that are both supermodular and coordinate-wise convex), which are extensively studied in the literature, are always PMAS kind. Several other solution concepts that further refine the Walrasian PMAS are also proposed and characterized. (joint work with Dong Liang and Ning Yu)

个人简介

曹志刚，北京交通大学经济永利教授。2010年毕业于中科院数学与系统科学研究院并留院任助理研究员。2017年9月加盟北京交通大学经济永利，任“卓越百人计划”教授。长期从事合作博弈、交通博弈、网络博弈和算法博弈等方面的研究，在包括Operations Research、Mathematics of Operations Research、Games and Economic Behavior、Journal of Mathematical Economics、Social Choice and Welfare、International Journal of Game Theory和《中国科学：数学》在内的期刊上发表多篇论文。相关成果曾获中国信息经济学理论贡献奖、系统科学与系统工程青年科技奖、中国决策科学青年科技奖和关肇直青年研究奖等荣誉。先后主持国家自然科学基金委的青年、面上和优青项目。兼任中国“双法”研究会智能决策与博弈分会副理事长，中国运筹学会博弈论分会副理事长，中国双法学会青年工作委员会副秘书长、网络科学分会副秘书长，中国信息经济学会常务理事和中国运筹学会理事等职务。