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arXiv · 2603.18304

Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information

Yuxiang Guan·Iman Shames·Tyler Summers
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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.

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Yuxiang Guan, Iman Shames, Tyler Summers. 2026-03-18. Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information. https://arxiv.org/abs/2603.18304

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