Nash Equilibrium Seeking for Noncooperative Duopoly Games via Event-Triggered Control

TL;DR

This paper introduces a model-free, event-triggered control method employing extremum seeking to achieve stable Nash equilibrium convergence in duopoly games, effectively balancing control performance and communication constraints.

Contribution

It presents the first integration of noncooperative game solving with event-triggered, model-free extremum seeking, ensuring stability under limited bandwidth.

Findings

Achieves local stability of Nash equilibrium using event-triggered control.

Quantifies residual set size around Nash equilibrium.

Demonstrates effectiveness through numerical example.

Abstract

This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal perturbation signals applied to estimate the Gradient (first derivative) of unknown quadratic payoff functions. This is the first instance of noncooperative games being tackled in a model-free fashion integrated with the event-triggered methodology. Each player evaluates independently the deviation between the corresponding current state variable and its last broadcasted value to update the player action, while they preserve control performance under limited bandwidth of the actuation paths and still guarantee stability for the closed-loop dynamics. In particular, the stability analysis is carried out using time-scaling technique, Lyapunov's direct method and averaging theory for discontinuous systems. We quantify the size of the ultimate small residual sets around the Nash equilibrium and illustrate the theoretical results numerically on an example.