A distributed generalized Nash equilibrium seeking algorithm based on extremum seeking control

TL;DR

This paper introduces a distributed, model-free algorithm combining extremum seeking control and learning to find generalized Nash equilibria in constrained noncooperative games without requiring knowledge of agents' cost functions or strategies.

Contribution

It proposes a novel distributed GNE seeking algorithm that leverages extremum seeking control, enabling agents to find equilibria without detailed system models or strategy information.

Findings

Algorithm successfully finds GNE in numerical examples.

The method converges non-locally under certain conditions.

It effectively handles coupled constraints with minimal information exchange.

Abstract

In this paper, a distributed non-model based seeking algorithm which combines the extremum seeking control (ESC) jointly with learning algorithms is proposed to seek a generalized Nash equilibrium (GNE) for a class of noncooperative games with coupled equality constraint. The strategy of each agent is restricted by both the coupled inter-agent constraint and local inequality constraints. Thanks to the ESC, it is unnecessary to know the specific expressions of agents' cost functions and local constraints and to know the strategies of other agents for the implementation of the proposed GNE seeking algorithm. To deal with the coupled constraints, only the Lagrange multiplier is transmitted among agents with some prior information about the coupled constraints. Moreover, a diminishing dither signal is designed in the seeking algorithm to remove undesirable steady-state oscillations. The non-local convergence of the designed seeking algorithm is analyzed via the singular perturbation theory, averaging analysis and Lyapunov stability theory. Numerical examples are given to verify the effectiveness of our proposed method.