在本文中，在一個有著外來干擾的平均場隨機系統上，我們研究一個有著不同目標策略的多個玩家的隨機非合作追蹤賽局和一個有著共同目標策略的多個玩家的隨機合作追蹤賽局。因為在系統動態和成本函數中的平均場行為，針對在平均場隨機帕松跳躍系統上的目標追蹤的非合作和合作賽局策略設計會比在傳統隨機系統上更加困難。以我們使用的間接方法，非合作和合作賽局策略設計問題分別被轉變成線性矩陣不等式所限制的多目標和單一目標問題。線性矩陣不等式所限制的多目標問題可以被納許均衡解來解決，而為了求解，我們使用線性矩陣不等式所限制的多目標進化演算法。兩個模擬範例包括在網絡社交系統上的股市分配和網路安全策略被用來顯示我們實行的演算法和所得到的策略的設計步驟和有效性。

The multi–player stochastic noncooperative tracking game (NTG) with conflicting target strategy and cooperative tracking game (CTG) with common target tracking strategy for the target tracking design problem of mean-field stochastic jump diffusion (MFSJD) system with external disturbance are investigated in this study. Due to the mean (collective) behaviour in the system dynamic and cost functional, the design of the NTG strategy and CTG strategy for target tracking of the MFSJD system are more difficult than the conventional stochastic system. By the proposed indirect method, the NTG and CTG strategy design problem are transformed into linear matrix inequalities (LMIs)–constrained multi-objective problem (MOP) and LMIs constrained single-objective problem (SOP), respectively. The LMIs–constrained MOP could be solved effectively for the Nash equilibrium solution of NTG by the proposed LMIs–constrained multi-objective evolutionary algorithm (MOEA). Two simulation examples including the share market allocation and network security strategies in cyber–social systems are given to illustrate the design procedure and validate the effectiveness of the proposed LMI–constrained MOEA for Nash equilibrium solution of NTG and CTG strategies of MFSJD system.

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