Time-varying constrained proximal type dynamics in multi-agent network games

TL;DR

This paper introduces a novel iterative algorithm for multi-agent network games with time-varying constraints and communication, ensuring convergence to equilibrium using only local information.

Contribution

It develops a new proximal dynamics-based algorithm for time-varying constrained games, addressing convergence issues in existing methods.

Findings

Algorithm converges to a class of game equilibria.

Validated through a constrained consensus problem.

Addresses convergence failure in original game dynamics.

Abstract

In this paper, we study multi-agent network games subject to affine time-varying coupling constraints and a time-varying communication network. We focus on the class of games adopting proximal dynamics and study their convergence to a persistent equilibrium. The assumptions considered to solve the problem are discussed and motivated. We develop an iterative equilibrium seeking algorithm, using only local information, that converges to a special class of game equilibria. Its derivation is motivated by several examples, showing that the original game dynamics fail to converge. Finally, we apply the designed algorithm to solve a constrained consensus problem, validating the theoretical results.