Gradient Dynamics in Linear Quadratic Network Games with Time-Varying Connectivity and Population Fluctuation

TL;DR

This paper studies how agents learn in dynamic network games with changing connectivity and population, showing convergence to equilibrium using gradient methods under randomness.

Contribution

It introduces a framework for analyzing gradient-based learning in time-varying network games with stochastic participation and proves convergence to Nash equilibrium.

Findings

Almost sure convergence of strategies to Nash equilibrium

High-probability guarantees for epsilon-Nash equilibrium in large populations

Validation through an online market application

Abstract

In this paper, we consider a learning problem among non-cooperative agents interacting in a time-varying system. Specifically, we focus on repeated linear quadratic network games, in which the network of interactions changes with time and agents may not be present at each iteration. To get tractability, we assume that at each iteration, the network of interactions is sampled from an underlying random network model and agents participate at random with a given probability. Under these assumptions, we consider a gradient-based learning algorithm and establish almost sure convergence of the agents' strategies to the Nash equilibrium of the game played over the expected network. Additionally, we prove, in the large population regime, that the learned strategy is an $\epsilon$-Nash equilibrium for each stage game with high probability. We validate our results over an online market application.