Nash Equilibrium Seeking for Noncooperative Duopoly Games via Event-Triggered Control
arxiv(2024)
摘要
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.
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