Fixed-Time Nash Equilibrium Seeking in Non-Cooperative Games

TL;DR

This paper proposes a new class of model-free Nash equilibrium seeking dynamics with fixed convergence time bounds, applicable to potential and strongly monotone games, using only real-time cost evaluations and neighbor communications.

Contribution

It introduces a novel fixed-time convergence dynamics for Nash seeking that is independent of initial conditions and requires only local cost evaluations and neighbor information.

Findings

Convergence to Nash equilibrium is guaranteed within a prescribed fixed time.

The proposed dynamics are applicable to potential and strongly monotone games.

Numerical examples validate the theoretical convergence properties.

Abstract

We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper bounded by a positive constant that is independent of the initial conditions of the players, and which can be prescribed a priori by the system designer. The dynamics are model-free, in the sense that the mathematical forms of the cost functions of the players are unknown. Instead, in order to update its own action, each player needs to have access only to real-time evaluations of its own cost, as well as to auxiliary states of neighboring players characterized by a communication graph. Stability and convergence properties are established for both potential games and strongly monotone games. Numerical examples are presented to illustrate our theoretical results.