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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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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