Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information
Abstract
We formulate and study a class of two-player zero-sum stochastic dynamic games with partial and asymmetric information. Information asymmetry introduces fundamental challenges involving \emph{belief representation} and \emph{theory of mind} issues, where agents must impute belief states and estimates of other agents to inform their own strategy. To avoid an infinite regress of higher-order beliefs amongst agents and obtain computationally implementable results, we focus on a linear quadratic Gaussian (LQG) model and consider strategies with limited internal state dimension. We present a novel iterative forward-backward algorithm to jointly compute belief states and equilibrium strategies and value functions for a finite-horizon problem. We also present a value iteration-like algorithm to jointly compute stationary belief states and equilibrium strategies for an average-cost infinite-horizon problem. An open-source implementation of the algorithms is provided, and we demonstrate the effectiveness of the proposed algorithms in numerical experiments.
Keywords
Cite
@article{arxiv.2603.18304,
title = {Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information},
author = {Yuxiang Guan and Iman Shames and Tyler Summers},
journal= {arXiv preprint arXiv:2603.18304},
year = {2026}
}