非线性随机系统在博弈问题中的应用研究

随机系统是控制理论中经常遇到的一类重要的系统.文中针对一类带有高斯白噪声的随机模型,通过福克普朗克方程,研究分析了随机系统的非平衡相变;借助2×2的演化博弈问题,通过数值模拟对比分析了随机因素给系统带来的影响.实验表明,随机因素会对博弈参与者产生影响.群体规模大,学习认知能力弱都会使得影响程度增大,经过足够的博弈时间,其稳态决策相似,这对实际决策问题具有重要的参考意义.

The application research of the nonlinear stochastic system in the game

Stochastic system is one of important systems in the control theory. In this paper, a stochastic model with Gaussian white noise are studied through the Fokker Planck equation; based on evolutionary game theory, comparative analysis for the influences of random factors on the system are done by numerical simulations. The experiments show that these factors have an impact on game players, but has affected conditions, which gives an important reference to the actual decision-making.