A Double-Layer Adaptive Scheme for Fully Distributed Nash Equilibrium Seeking

We present a fully distributed Nash equilibrium seeking strategy by designing a double-layer adaptive control law in this paper, by which players can update their actions without knowing any global information. In comparison with existing fully distributed approaches, the proposed algorithm employs a damping term in the adaptive parameter design, which is more preferable for practical implementations as it avoids continuously increasing adaptive gains. Analytical analysis on the convergence of the designed strategy is carried out by Lyapunov stability analysis, and it is verified that the Nash equilibrium is globally asymptotically stable by using the proposed algorithm. The effectiveness of the proposed method is illustrated by a numerical example finally.