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微分对策中的联盟解
引用本文:彼得罗相.微分对策中的联盟解[J].运筹学学报,2012,16(4):86-94.
作者姓名:彼得罗相
作者单位:1. St. Petersburg University, Universitetsky pr. 35
摘    要:提出时间区间t_0,∞)上的n人微分对策两阶段联盟解. 在第一阶段不能形成大联盟的假设是自然的,即源于这一思想. 在第一阶段以联盟作为局中人的对策中计算得到其纳什均衡,之后对每个联盟的收益按Shapley值进行分配. 一个n人微分减排模型的例子阐明了上述结果.

关 键 词:微分对策  Hamilton--Jacobi--Bellman方程  联盟剖分  Shapley值  Nash均衡  PMS-值  

Coalitional solutions in differential games
Leon A.Petrosyan.Coalitional solutions in differential games[J].OR Transactions,2012,16(4):86-94.
Authors:Leon APetrosyan
Institution:1. St. Petersburg University, Universitetsky pr. 35
Abstract:The two-stage (level) coalitional solution for n-person differential game played over the time interval t_0,∞) is proposed. The paper emerges from the
idea that it is natural not to assume that coalitions on the first level can form a grand coalition. At first level the Nash equilibrium in the game played by coalitions is computed. Secondly the value of each coalition is allocated according to the Shapley value. The results are illustrated by an example of n-person differential emission reduction model.
Keywords:differential game  Hamilton-Jacobi-Bellman equation  coalitional partition  Shapley value  Nash equilibrium  PMS-value
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