动态合作博弈中解的策略稳定性

【作者】 王磊；

【导师】 高红伟；

【作者基本信息】 青岛大学 ， 管理科学与工程， 2016， 博士

【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。更多还原

【Abstract】 Cooperation is the basis of human civilization. The global economy shows deep cross-integration with the deep development of social information and the rise of the Internet economy. Cooperative game has become the forefront of international management scientific research.This paper will focus on the strategic stability of solutions for the dynamic cooperative game, in which the time consistency is the starting point and the networked contact of players and the uncertainty(randomness) of the game process are the main features. The methods of constructing Nash or strong Nash equilibrium are proposed and existence theorems of equilibrium are proved for different dynamic cooperative games, which guarantee the strategic stability of long-range cooperative agreements. The main works in this dissertation include:Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments. From these, the time-consistent cooperative agreement can be strategically supported by epsilon-Nash or strong epsilon-Nash equilibrium. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibrium can be constructed. Based on imputation distribution procedures, a model of infinite stage game with a coalition structure is proposed. The existence of Nash or strong Nash equilibrium in such a game is proved, which guarantees the strategic support of cooperation. A kind of new characteristic function is defined which enables an equilibrium to be constructed in the case with delayed strategies. We provide conditions when the cooperative behavior resulting in the dynamic Shapley value can be supported by a strong Nash equilibrium. We propose trigger strategies for coalition deviation from cooperation and prove the existence of a strong epsilon-perfect equilibrium for the class of stochastic games played over event trees.The theory is adopted for the repeated Prisoner’s dilemma game which is a classical problem of dynamic games. This research can innovate and develop the cooperative game theory, shorten the gap between theory and practice.更多还原