动态合作博弈中解的策略稳定性

发布时间：2018-04-27 02:31

本文选题：动态合作博弈 + 策略稳定性　；参考：《青岛大学》2016年博士论文

【摘要】：合作是人类文明的基础。社会信息化的深入发展与互联网经济的兴起,使全球经济呈现出深度的交叉融合。合作博弈亦成为国际管理科学研究前沿。本文以动态合作博弈的时间一致性理论为切入点,以主体联系的网络化、博弈进程的不确定性(随机性)为视角和主要特征,聚焦研究动态合作博弈解的策略稳定性问题,针对几类不同的动态合作博弈模型,提出构建Nash或强Nash均衡的方法,证明均衡的存在性定理,保证合作的策略支撑。论文的主要工作包括:基于分配补偿程序提出具有联盟结构的合作微分博弈模型,对动态环境中的群体偏离做出差异时刻一致性的假设,并证明时间一致的合作协议能够通过ε-Nash或强ε-Nash均衡策略支撑;在具有联盟结构的完美信息扩展型合作博弈中构建Nash或强Nash均衡;建立具有联盟结构的无限阶段合作博弈模型,证明Nash和强Nash均衡的存在性;定义一类广义特征函数,研究策略延迟的情形,给出Nash和强Nash均衡的构造;针对初始阶段为网络生成的网络上的动态合作博弈,给出动态Shapley值能被强Nash均衡策略支撑的的充分性条件;针对有限历程事件树上的动态合作博弈,提出局中人针对联盟偏离的惩罚策略,建立强ε-Nash均衡存在的充分性条件。理论应用到重复囚徒困境经典博弈问题。研究成果丰富和发展了合作博弈理论,缩短了理论与实践的差距。
[Abstract]:Cooperation is the foundation of human civilization. With the development of social informatization and the rise of Internet economy, the global economy presents a deep cross-integration. Cooperative game has also become the frontier of international management science research. This paper focuses on the strategic stability of the solution of dynamic cooperative game from the point of view of the time consistency theory of dynamic cooperative game, the networking of the subject connection, the uncertainty (randomness) of the process of the game. Aiming at several kinds of dynamic cooperative game models, a method of constructing Nash or strong Nash equilibrium is proposed, the existence theorem of equilibrium is proved, and the strategy support of cooperation is guaranteed. The main work of this paper includes: a cooperative differential game model with alliance structure is proposed based on the allocation and compensation program, and the assumption that the group deviates from each other in the dynamic environment is consistent at different times. It is proved that cooperative protocols with consistent time can be supported by 蔚 -Nash or strong 蔚 -Nash equilibrium strategies, construct Nash or strong Nash equilibrium in extended cooperative game with perfect information with alliance structure, and establish infinite stage cooperative game model with alliance structure. The existence of Nash and strong Nash equilibrium is proved, a class of generalized eigenfunctions is defined, the case of strategy delay is studied, and the construction of Nash and strong Nash equilibrium is given. The sufficient condition that the dynamic Shapley value can be supported by the strong Nash equilibrium strategy is given, and the sufficient condition for the existence of strong 蔚 -Nash equilibrium is established for the dynamic cooperative game in the event tree of finite course. The theory is applied to the classical game of the repeated prisoner's dilemma. The research results enrich and develop the cooperative game theory and shorten the gap between theory and practice.
【学位授予单位】：青岛大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224.32

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