Construction and Implementation of Stochastic Nash Equilibrium for Large-Scale Systems with Noise

本文研究了一类不确定大系统的纳什均衡问题。在用伊藤微分方程描述不确定性之后，为了达到随机纳什均衡和获得策略集，建立了一些条件和数值算法。与已有结果比较表明，即使存在建模误差和环境变化带来的不确定性，纳什均衡策略也是可以设计的。此外，通过数值模拟验证了所提方法的有效性。

In this study, the Nash equilibrium problem for a class of large-scale uncertain systems has been addressed. After describing the uncertainties by means of Ito differential equation, in order to attain the stochastic Nash equilibrium and to obtain the strategy set some conditions and numerical algorithms have been established. As compared with the existing results, even if there exist the modeling errors and the uncertainty due to the variation of environment, it has been shown that the Nash equilibrium strategy can be designed. Moreover, the proposed methodology has been confirmed via the numerical simulation.