引用本文:余国林, 刘三阳,李炳杰.多组对策系统非劣Nash策略的最优均衡解算法[J].控制理论与应用,2007,24(5):785~789.[点击复制]
YU Guo-lin, LIU San-yang, LI Bing-jie.Optimal equilibrium solution algorithm for non-inferior Nash strategies in multi-team game systems[J].Control Theory and Technology,2007,24(5):785~789.[点击复制]
多组对策系统非劣Nash策略的最优均衡解算法
Optimal equilibrium solution algorithm for non-inferior Nash strategies in multi-team game systems
摘要点击 1475  全文点击 1256  投稿时间：2004-11-24  修订日期：2007-03-19
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DOI编号  10.7641/j.issn.1000-8152.2007.5.017
  2007,24(5):785-789
中文关键词  多组对策  非劣Nash策略  最优均衡值  最优均衡解
英文关键词  multi-team games  non-inferior Nash strategy  optimal equilibrium payment  optimal equilibrium solution
基金项目  国家自然科学基金资助项目(60674708); 陕西省自然科学研究资助项目(2004A05).
作者单位
余国林, 刘三阳,李炳杰 西安电子科技大学理学院数学系, 陕西西安710071
空军工程大学理学院, 陕西西安710051 
中文摘要
      多组对策系统中求解组与组之间的非劣Nash策略至关重要. 如何针对一般问题解析求出非劣Nash策略还没有有效的方法. 本文阐述了一种利用组与组之间的非劣反应集构造求解非劣Nash策略的迭代算法. 为此首先引进多组对策系统组内部合作对策的最优均衡值和最优均衡解的概念, 然后通过证明最优均衡解是组内部隐含某一权重向量的合作对策的非劣解, 得到求解合作对策的单目标规划问题. 进一步说明在组内部该问题的解不仅是非劣解而且对所有局中人都优于不合作时的Nash平衡策略. 最后给出了验证该算法有效性的一个实际例子.
英文摘要
      The solution of non-inferior Nash strategy between the teams plays an important role in multi-team game systems. Unfortunately there is no effective way to obtain an analytic solution for general problems. Motivated by the non-inferior reaction sets of the games, a general construction iterative algorithm for solving non-inferior Nash strategies is proposed. Firstly, the notions called optimal equilibrium payment and optimal equilibrium solution for cooperative games within each team in multi-team game systems are introduced. Then, by proving that the optimal equilibrium solution is a non-inferior solution for cooperative game which implies a certain weight vector within each team, a single objective programming for solving the cooperative games within each team is developed. It is shown that the solution of this programming is not only the non-inferior solution but also the strategy being superior to Nash equilibrium strategies for all the players within each team. Finally, an example is given to illustrate the effectiveness of the algorithm.