基于仿真的博弈系统优化策略研究

发布时间：2018-07-06 15:22

本文选题：仿真 + 凸优化　；参考：《上海理工大学学报》2017年05期

【摘要】：以石头剪刀布博弈系统为例,提出一种新的理论方法优化该系统,目的是在不受其他因素影响下最大化玩家获得的收益,这种新方法即凸优化.引入非零和矩阵建立凸优化算法模型,定量地创建了石头剪刀布博弈系统收益方程,这种方法前人鲜有研究.创新地提出了博弈系统最优值的临界方程即鞍点方程,并用强对偶理论证明了该方程的正确性.重点研究凸优化中的Newton算法对石头剪刀布博弈系统进行数据仿真和最大化玩家获得的收益.仿真结果表明,数值结果与理论假设相一致,验证了该方法的可行性和正确性.该研究对于理解博弈系统和应用凸优化具有十分重要的意义.
[Abstract]:Taking the game system of rock scissors and scissors as an example, a new theoretical method is proposed to optimize the system. The aim is to maximize the player's income without the influence of other factors. This new method is convex optimization. The convex optimization algorithm model is established by introducing the nonzero sum matrix, and the profit equation of rock scissors cloth game system is established quantitatively. This method has not been studied before. The critical equation of the optimal value of the game system, the saddle point equation, is proposed in this paper, and the correctness of the equation is proved by using the strong duality theory. This paper focuses on the Newton algorithm in convex optimization to simulate the game system and maximize the player's income. The simulation results show that the numerical results agree with the theoretical assumptions and verify the feasibility and correctness of the method. This research is very important for understanding game system and applying convex optimization.
【作者单位】：上海理工大学理学院;
【基金】：国家自然科学基金资助项目(10874118)
【分类号】：O225

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