Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information
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| Format: | Preprint |
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2026
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| _version_ | 1866914408594145280 |
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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 |