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

Fuente: arXiv
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Main Authors: Guan, Yuxiang, Shames, Iman, Summers, Tyler
Format: Preprint
Published: 2026
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author Guan, Yuxiang
Shames, Iman
Summers, Tyler
author_facet Guan, Yuxiang
Shames, Iman
Summers, Tyler
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_18304
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information
Guan, Yuxiang
Shames, Iman
Summers, Tyler
Optimization and Control
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.
title Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information
topic Optimization and Control
url https://arxiv.org/abs/2603.18304