  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.
