Year: 2026
Type: article
Abstract: This work studies a class of zero-sum stochastic linear quadratic dynamic games (LQDGs) under partial and asymmetric information. Information asymmetry introduces fundamental challenges related to belief representation and theory of mind, where players must impute belief states and estimates of other players to inform their strategies. Existing work highlights the difficulty of applying a dynamic programming-like decomposition approach to these problems. An alternative approach based on best response dynamics is proposed, which provides insights into belief representation and theory of mind challenges. Explicit expressions for each player’s best response within the class of pure linear dynamic output feedback control strategies are derived, where the internal state dimension of each control is an integer multiple of the system state dimension. As players iteratively update their best responses, they form increasingly higher-order belief states, leading to infinite-dimensional internal states. However, numerical results reveal that the game’s value converges after only a few iterations, suggesting that higher-order belief states provide vanishing benefit. This work further conducts numerical experiments to analyze the impact of asymmetric beliefs, belief orders, relative controllability and observability, and direct feed-through on a linear quadratic pursuit–evasion game’s value.
DOI: 10.2514/1.g009807
Authors: Yuxiang Guan, Iman Shames, Tyler H. Summers
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7203630761
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