一种连续型不确定性复杂系统博弈理论及算法研究  

Research on game theory and algorithm for a continuous uncertain complex system

作　　者：曹黎侠[1] 祝士杰 CAO Lixia;ZHU Shijie(School of Fundamentals,Xi’an University of Technology,Xi’an 710021,China)

机构地区：[1]西安工业大学基础学院,西安710021

出　　处：《重庆理工大学学报（自然科学）》2024年第5期121-129,共9页Journal of Chongqing University of Technology：Natural Science

基　　金：陕西省科技厅基金项目(KRM056)。

摘　　要：当前对于不确定性复杂系统博弈的研究,通常情况下有关策略集是离散的,而非连续和随机的。而在复杂经济社会系统中,常常会遇到连续性随机博弈问题,以及系统中数据的确权问题。在此背景下,提出了一种随机博弈的概念,给出连续策略集下N人非合作随机博弈模型均衡解存在性定理,以及复杂信息系统随机博弈模型的构建及其纳什均衡解算法。给出连续策略下不确定性N人非合作随机博弈概念,建立以局中人的最大收益为目标函数的N人非合作随机博弈模型,提出了均衡解的存在性定理;构建了Wasserstein模糊集,之后融合分布鲁棒优化方法以及投资组合优化方法将该模型转化为有限凸规划,并运用遗传算法求解局中人的近似混合策略,最后构建了基于回归分析的纳什均衡求解算法并将纳什均衡解归一化进行确权。实证分析表明,所构建的理论与算法是有效可行的。The current research on game theory in uncertain complex systems typically involves a discrete set of strategies rather than continuous and random ones.In complex economic and social systems,continuous stochastic game problems and data ownership issues are often encountered.Against such a backdrop,this paper proposes a concept of stochastic game,builds a non-cooperative stochastic game model under a continuous strategy set and presents its Nash equilibrium solution algorithm.Firstly,the concept of non-cooperative stochastic game with uncertainty under continuous strategy is proposed,and a non-cooperative stochastic game model with the objective function of maximizing the payoff of players is built.The existence theorem of equilibrium solutions is also proposed.We build the Wasserstein fuzzy set,which is then transformed into a finite convex programming model by integrating distributed robust optimization methods with portfolio optimization methods.The genetic algorithms are employed to solve the approximate mixed strategy of the players in the game.Finally,a Nash equilibrium solution algorithm is built based on regression analysis and normalized the Nash equilibrium solution for weight confirmation.Our empirical analysis shows the theory and algorithm proposed in this article are effective and feasible.

关 键 词：纳什均衡解 Wasserstein模糊集 分布鲁棒优化方法 有限凸规划 遗传算法 

分 类 号：O225[理学—运筹学与控制论]