标题：Dynamics and stability for a class of evolutionary games with time delays in strategies
作者：Wang, Yuanhua; Cheng, Daizhan
作者机构：[Wang Yuanhua] School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China.;[Cheng Daizhan] School of Control Scienc 更多
通讯作者地址：[Wang, YH]Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China;[Wang, YH]Qilu Normal Univ, Coll Phys & Elect Engn, Jinan 250013, Peopl 更多
关键词：evolutionary game; time delays; potential game; semi-tensor product of; matrices; stability
摘要：This paper investigates the modeling and stability of a class of finite evolutionary games with time delays in strategies. First, the evolutionary dynamics of a sequence of strategy profiles, named as the profile trajectory, is proposed to describe the strategy updating process of the evolutionary games with time delays. Using the semi-tensor product of matrices, the profile trajectory dynamics with two kinds of time delays are converted into their algebraic forms respectively. Then a sufficient condition is obtained to assure the stability of the delayed evolutionary potential games at a pure Nash equilibrium.