A distributed singular perturbation algorithm in a non-cooperative game under limited control authority

Abstract

Abstract This paper proposes a distributed algorithm to seek Nash equilibrium (NE) in a non-cooperative game under limited control authority (LCA). Our proposed strategy relies upon singular perturbed system and dynamic average consensus algorithm. The distributed algorithm is designed so that every player can precisely estimate actions of other players in the game under the LCA, then follows a gradient-based method to reach NE. We also provide a convergence proof of the algorithm to a NE of the game. Numerical simulation is finally carried out to verify the effectiveness of our design.