Distributed Event-Triggered Nash Equilibrium Seeking for Noncooperative Games

TL;DR

This paper introduces a novel distributed event-triggered algorithm for Nash equilibrium seeking in noncooperative games, using model-free pseudo-gradient estimates and sinusoidal perturbations, ensuring convergence and stability.

Contribution

It presents the first model-free, event-triggered extremum seeking approach for noncooperative games with guaranteed convergence and Zeno behavior avoidance.

Findings

Guarantees convergence to Nash equilibrium

Ensures Zeno behavior is avoided with minimum dwell-time

Validated through numerical simulations in an oligopoly setting

Abstract

We propose locally convergent Nash equilibrium seeking algorithms for $N$-player noncooperative games, which use distributed event-triggered pseudo-gradient estimates. The proposed approach employs sinusoidal perturbations to estimate the pseudo-gradients of unknown quadratic payoff functions. This is the first instance of noncooperative games being tackled in a model-free fashion with event-triggered extremum seeking. Each player evaluates independently the deviation between the corresponding current pseudo-gradient estimate and its last broadcasted value from the event-triggering mechanism to tune individually the player action, while they preserve collectively the closed-loop stability/convergence. We guarantee Zeno behavior avoidance by establishing a minimum dwell-time to avoid infinitely fast switching. In particular, the stability analysis is carried out using Lyapunov's method and averaging for systems with discontinuous right-hand sides. We quantify the size of the ultimate small residual sets around the Nash equilibrium and illustrate the theoretical results numerically on an oligopoly setting.