具有状态支付向量的有向图上的动态对策  

Dynamic Game in Directed Graph with State Payoff Vector

作　　者：于琨[1] 高红伟[1] 王桂熙[1] 杨慧敬[1] 

机构地区：[1]青岛大学数学科学学院,青岛市宁夏路308号266071

出　　处：《青岛大学学报（自然科学版）》2008年第2期14-17,21,共5页Journal of Qingdao University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(编号:70571040;70711120204)

摘　　要：通过在有向图的每个状态结点处引入状态支付向量,运用C.Berge关于图上对策中策略的概念,在有限图上研究动态对策。在非合作情形,证明了具有状态支付向量的有向图上对策的精练均衡的存在性定理。在合作情形,通过建立有向图上局与对策树上路径之间的对应关系,将有向图上的对策转化为对策树,并给出了特征函数的算法以及以Shapley向量作为合作解的计算示例。State payoff vector is introduced to every state node in directed graph in this paper. The concept of strategy of game in graph defined by C. Berge is introduced to study dynamic game in finite graph. In the case of non-cooperation, the existence theorem on subgame refined equilibrium is given for directed graph with state payoff vector. While in the case of cooperation, by establishing the relations between station in directed graph and path in game tree, the game on directed graph is transformed to the game tree, furthermore algorithm of characteristic function and examples using Shapley vector as cooperative solution are given.

关 键 词：有向图 状态支付向量 简单策略 特征函数 Shapley向量 

分 类 号：O225[理学—运筹学与控制论]