Extension of standard game dynamics and its applications

我们将标准的博弈动力学扩展到N人博弈动力学，马尔可夫博弈动力学和连续博弈动力学，并根据动力系统理论研究它们。(1)N人游戏动态：该模型被描述为耦合映象格子和全局耦合映象，表现出复杂的非线性行为，如行波、时空混沌、时空不稳定等。(2)马尔可夫博弈动态：玩家不是由概率分布建模，而是由简单的马尔可夫系统建模。我们从动力系统理论和信息理论两个方面对它们进行了分析。(3)连续博弈动态：连续行动的混合策略被建模为概率密度函数，并构建了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.