Learning with Delayed Payoffs in Population Games using Kullback-Leibler Divergence Regularization

TL;DR

This paper introduces the Kullback-Leibler Divergence Regularized Learning (KLD-RL) model for population games with delays, ensuring convergence to Nash equilibrium without oscillations through passivity-based analysis.

Contribution

It proposes a novel KLD-RL model with an iterative regularization algorithm that guarantees convergence in delayed population games, addressing a key challenge in multi-agent learning.

Findings

KLD-RL converges to Nash equilibrium despite delays.

The model prevents oscillations in strategy updates.

Numerical experiments confirm theoretical results.

Abstract

We study a multi-agent decision problem in large population games. Agents from multiple populations select strategies for repeated interactions with one another. At each stage of these interactions, agents use their decision-making model to revise their strategy selections based on payoffs determined by an underlying game. Their goal is to learn the strategies that correspond to the Nash equilibrium of the game. However, when games are subject to time delays, conventional decision-making models from the population game literature may result in oscillations in the strategy revision process or convergence to an equilibrium other than the Nash. To address this problem, we propose the Kullback-Leibler Divergence Regularized Learning (KLD-RL) model, along with an algorithm that iteratively updates the model's regularization parameter across a network of communicating agents. Using passivity-based convergence analysis techniques, we show that the KLD-RL model achieves convergence to the Nash equilibrium without oscillations, even for a class of population games that are subject to time delays. We demonstrate our main results numerically on a two-population congestion game and a two-population zero-sum game.