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无限阶段网络博弈中合作解的策略稳定性

王磊1,3  林崇3,4  谷岩1 刘翠1 高红伟1,2,*   

  1. 1. 青岛大学数学与统计学院, 山东青岛 266071; 2. 山东省应用数学研究所, 山东青岛 266071;
     
    3. 青岛大学自动化与电气工程学院, 山东青岛  266071; 4. 青岛大学复杂性科学研究所, 山东青岛 266071   
  • 收稿日期:2015-07-16 出版日期:2018-03-15 发布日期:2018-03-15
  • 通讯作者: 高红伟 E-mail: cmgta2007@163.com
  • 基金资助:

    国家自然科学基金面上项目(No. 71571108), 国家自然科学基金国际(地区)合作交流项目(Nos. 71611530712, 61661136002), 中国博士后科学基金面上资助项目(No. 2016M600525), 青岛市博士后应用研究项目(No. 2016029)

Strategic stability of cooperative solutions in infinite stage network games

 WANG Lei1,3   LIN Chong3,4   GU Yan1  LIU Cui1 GAO Hongwei1,2,*   

  1. 1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, Shandong, China; 2. Institute of Applied Mathematics,  Qingdao, 266071, Shandong, China; 3. College of Automation and Electrical Engineering, Qingdao University,  Qingdao, 266071, Shandong,  China; 4. Institute of Complexity Science, Qingdao University, Qingdao, 266071, Shandong, China
  • Received:2015-07-16 Online:2018-03-15 Published:2018-03-15

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摘要：

合作博弈的经典合作解不满足时间一致性, 并缺乏策略稳定性. 本文研究无限阶段网络博弈合作解的策略稳定性理论. 首先建立时间一致的分配补偿程序实现合作解的动态分配, 然后建立针对联盟的惩罚策略, 给出合作解能够被强Nash均衡策略支撑的充分性条件, 最后证明了博弈中的惩罚策略局势是强Nash均衡, 从而保证了合作解的策略稳定性. 作为应用, 考察了重复囚徒困境网络博弈中Shapley值的策略稳定性.

关键词: 网络博弈, 合作解, 分配补偿程序, 策略稳定性, 强Nash均衡

Abstract:

The classical cooperative solutions of cooperative games are not time consistent and lack of strategic stability. The theory of strategic stability of cooperative solutions is studied for infinite stage network games. We build the time consistent imputation distribution procedure to realize the dynamic allocation of the cooperative solution, propose the penalty strategies for coalitions, and provide conditions from which the cooperative solution can be supported by a strong Nash equilibrium. The penalty strategy profile in the game is proved to be a strong Nash equilibrium, which ensures the strategic stability of cooperative solutions. The strategic stability of Shapley value in the repeated prisoners dilemma network game is studied as an application of the theory.

Key words: network game, cooperative solution, imputation distribution procedure, strategic stability, strong Nash equilibrium