Modeling and Stability Analysis of Delayed Game Network

This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler’s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game’s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result. Keywords—Game networks, zero-sum game, delayed singular system, nonlinear perturbation, time delay.