合作对策的解在新的最优准则下的构造及对策模型

【作者】 乔晗；

【导师】 田志远；

【作者基本信息】 青岛大学 ， 基础数学， 2005， 硕士

【摘要】 本文分为三章。第一章针对于经典静态合作对策中效用不可转移的对策(NTU对策)建立了弱优超与弱稳定集的概念,对NTU对策核心中的支付进行了精炼,并讨论了所有不能被弱优超的支付的全体所组成的集合与核心、弱稳定集三者的关系。 第二章和第三章建立在具有完全信息的有限扩展型对策基础上。局中人以维护自己所在的联盟利益为行为准则,即采取策略使得其所在联盟总收益最大。定义了对非合作Nash均衡的最优反应,并以此为原则建立特征函数,在局中人对个体合理性的要求无法保障的情况下采用核子(Nucleolus)的方式在对策中建立动态最优解,并给出最优解以及最优路径的算法。 第二章具体研究了具有完全信息和变化联盟结构的有限动态合作对策。针对于在对策树给定的有限个节点上随机改变联盟剖分的动态对策,通过引入新的特征函数和最优准则,建立了其动态最优解PGN向量,并给出最优路径的算法。 第三章具体研究了具有完全信息的有限扩展型联合对策。针对于在对策开始的阶段首先形成所有可能的联盟剖分过程的联合对策,构造出了最优联盟剖分。通过引入新的特征函数和最优准则,建立动态最优解PGN向量,同时给出最优路径的算法。更多还原

【Abstract】 This thesis is composed of three chapters. In the first chapter, the concepts of weak dominance and weak stable set in classical static cooperative game without side payment(NTU game) are defined; the payoffs of cores in NTU games are refined. And relations of core, weak stable set and payoffs vector sets that cannot be weakly dominated are discussed.Games in extensive form with perfect information are considered in the second and third chapter. The player adopts the behavior rules which maintain profits of coalitions they belong to, namely, the player chooses strategies which maximize the sum of payoffs of coalitions. The concept of the best response to Nash Equilibrium of noncooperative game and characteristic functions based on this are defined. By introducing nueleolus, the dynamic optimal solution(PGN vector) is given and algorithm for the solution as well as optimal subtree (bunch) is established when individual rationality cannot be met.Concretely, finite dynamic cooperative game with perfect information and changing coalitional structures is considered in the second chapter. For dynamic game that randomly changes coalition partitions at limited fixed nodes of the game tree, the dynamic optimal solution (PGN vector) and the algorithm for constructing the optimal subtree (bunch) are given by introducing new defined character functions and optimal rules.In the third chapter, the coalitional game of finite extensive form with perfect information is considered. For coalitional games that form all coalitional partitions at beginning phase, optimal coalitional partition is constructed. The dynamic optimal solution and the algorithm for the optimal subtree (bunch) are given by introducing new defined character functions and optimal rules.更多还原