Fixed-Time Consensus-Based Nash Equilibrium Seeking

Dear Editor, This letter examines the fixed-time stability of the Nash equilibrium (NE) in non-cooperative games. We propose a consensus-based NE seeking algorithm for situations where players do not have perfect information and communicate via a topology graph. The proposed algorithm can achieve NE in a fixed time that does not depend on initial conditions and can be adjusted in advance. In this strategy, players use their estimates of other players' actions to update their own actions. We present sufficient conditions that ensure the fixed-time stability of the NE through rigorous Lyapunov stability analysis. Finally, we provide an example to verify the feasibility of the theoretical result.