We analyze best response dynamics for finding a Nash equilibrium of an infinite horizon zero-sum stochastic linear quadratic dynamic game (LQDG) with partial and asymmetric information. We derive explicit expressions for each player's best response within the class of pure linear dynamic output feedback control strategies where the internal state dimension of each control strategy is an integer multiple of the system state dimension. With each best response, the players form increasingly higher-order belief states, leading to infinite-dimensional internal states. However, we observe in extensive numerical experiments that the game's value converges after just a few iterations, suggesting that strategies associated with increasingly higher-order belief states eventually provide no benefit. To help explain this convergence, our numerical analysis reveals rapid decay of the controllability and observability Gramian eigenvalues and Hankel singular values in higher-order belief dynamics, indicating that the higher-order belief dynamics become increasingly difficult for both players to control and observe. Consequently, the higher-order belief dynamics can be closely approximated by low-order belief dynamics with bounded error, and thus feedback strategies with limited internal state dimension can closely approximate a Nash equilibrium.
Smart Jammer and LTE Network Strategies in An Infinite-Horizon Zero-Sum Repeated Game with Asymmetric and Incomplete Information
Intel Corporation（英特尔公司）；Georgia Institute of Technology（佐治亚理工学院）；Florida A&M University - Florida State University College of Engineering（佛罗里达农工大学-佛罗里达州立大学工程学院）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Asymmetric-Information Resource Allocation Games: An LP Approach to Purposeful Deception
School of Aerospace Engineering, Georgia Institute of Technology（佐治亚理工学院航空航天工程学院）；College of Engineering and Computing, George Mason University（乔治梅森大学工程与计算学院）
