Linear convergence in time-varying generalized Nash equilibrium problems
Optimization and Control
2023-04-20 v1 Computer Science and Game Theory
Multiagent Systems
Abstract
We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.
Keywords
Cite
@article{arxiv.2304.09593,
title = {Linear convergence in time-varying generalized Nash equilibrium problems},
author = {Mattia Bianchi and Emilio Benenati and Sergio Grammatico},
journal= {arXiv preprint arXiv:2304.09593},
year = {2023}
}