Partition-based Stability Concepts and a Partial Order that Links Risk Aversion to Cooperation
时 间：2023年8月17日 （周四）上午 10:00-11:30
地 点：澳门永利唯一官方网址 A523会议室
We are concerned with the stability of a coalitional game, i.e., a transferable-utility cooperative game. For us, the stability of a state should be about the difficulty to leave it once there. Following this guideline, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings. This principle of consensual blocking, as well as the traditional core-defining one of unilateral blocking and one straddling in between, can all be applied to partition-allocation pairs. Each such pair is made up of a partition of the grand coalition and a corresponding allocation vector whose components are efficient and individually rational for the various constituent coalitions of the given partition. Among the resulting stability concepts, two are universal in that any game, no matter how ``poor'' it is, has its fair share of stable solutions. For a game possessing strictly positive values, furthermore, its imputations would have fractional interpretations. These would allow a certain ranking between games, which we deem as in the sense of "centripetality", to imply a clearly describable shift in the games' stable solutions. When coalitions' values are built on both random outcomes and a common positively homogeneous reward function characterizing players' enjoyments from their shares, this comparative statics could help explain why aversion to risk often promotes cooperation.
Dr. Jian Yang obtained his Ph.D. in Management Science from the University of Texas at Austin. After working for the Department of Mechanical and Industrial Engineering at New Jersey Institute of Technology, he is now a professor at the Department of Management Science and Information Systems, Rutgers Business School, Rutgers University. Dr. Yang’s research interests are in combinatorial optimization, logistics, production and inventory control, dynamic pricing, and game theory. At the present he is particularly interested in the role played by risk and ambiguity in dynamic inventory-price control and game-theoretical settings.