Nash Equilibrium Estimation of Non-Cooperative Games with Time-Varying Delay

Time delay has great impacts on the stability and the reliability and real-time of the communication of multi-agent systems. In multi-agent communication network, due to network congestion, transmission distance and other factors, there are various communication delays. In this paper, we study the deviation of convergence value after adding time-varying delays under gradient descent method, and the upper bound related to delay time is estimated. This upper bound can be used to analyze the magnitude of deviation under different time delays and minimize the loss caused by delays, and provide more explicit information for system optimization and resource allocation. Numerical simulation is conducted to verify the proposed approach.