Extension of standard game dynamics and its applications

我们将标准博弈动力学扩展到n人博弈动力学、马尔可夫博弈动力学和连续博弈动力学，并从动力学系统理论的角度对它们进行了研究。(1) n人博弈动力学：该模型被描述为耦合地图点阵和全局耦合地图，并表现出行波、时空混沌、时空间歇性等复杂的非线性行为。(2)马尔可夫游戏动态：玩家不是通过概率分布建模，而是通过简单的马尔可夫系统。我们从理论和信息两方面对它们进行了分析。(3)连续博弈动力学：将连续行动的混合策略建模为概率密度函数，构建PDE模型。

We extend the standard game dynamics to N-person game dynamics, Markov game dynamics, and continuous game dynamics and study them in terms of dynamical systems theory. (1) N-person game dynamics : The model is described as coupled map lattice and globally coupled maps, and shows complex nonlinear behavior such as traveling waves, spatiotemporal chaos, spatiotemporal intermittency. (2) Markov game dynamics : Players are modeled not by probability distributions, but by simple Markov systems. We analyze them dynamical systems theoretically and information theoretically. (3) Continuous game dynamics : Mixed strategies for continuous actions are modeled as probability density functions and a PDE model is constructed.