While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy iteration algorithm for approximating the mean-field equilibrium in linear-quadratic MFGs with discounted cost. Given the mean-field, each agent faces a linear-quadratic tracking problem, the solution of which involves a dynamical system evolving in retrograde time. This makes the development of forward-in-time algorithm updates challenging. By identifying a structural property of the mean-field update operator, namely that it preserves sequences of a particular form, we develop a forward-in-time equilibrium computation algorithm. Bounds that quantify the accuracy of the computed mean-field equilibrium as a function of the algorithm's stopping condition are provided. The optimality of the computed equilibrium is validated numerically. In contrast to the most recent/concurrent results, our algorithm appears to be the first to study infinite-horizon MFGs with non-stationary mean-field equilibria, though with focus on the linear quadratic setting.
Intent Demonstration in General-Sum Dynamic Games via Iterative Linear-Quadratic Approximations
Oden Institute, University of Texas at Austin（德克萨斯大学奥斯汀分校奥登研究所）；Department of Economics, Stanford University（斯坦福大学经济学系）；Department of Electrical Engineering and Computer Sciences, University of California, Berkeley（加州大学伯克利分校电气工程和计算机科学系）；School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机学院）
A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games
Rotterdam School of Management, Erasmus University（鹿特丹管理学院，伊拉斯姆斯大学）；Division of Decision and Control Systems, KTH Royal Institute of Technology（决策与控制系，皇家理工学院）；Delft Center for Systems and Control, Delft University of Technology（系统与控制中心，代尔夫特理工大学）
Linear-Quadratic Gaussian Games with Distributed Sparse Estimation
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Oden Institute for Computational Engineering and Sciences（奥登计算工程与科学学院）；DEVCOM Army Research Laboratory（美军研究开发司令部陆军研究实验室）
Characterization and Computation of Feedback Nash Equilibria in Scalar Discounted N-Player Linear Quadratic Games
IMT School for Advanced Studies Lucca（卢卡高等研究院）；Research Unit DYSCO (Dynamical Systems, Control, and Optimization) at IMT School for Advanced Studies Lucca（卢卡高等研究院动态系统、控制与优化研究单元）
Policy Optimization Provably Converges to Nash Equilibria in Zero-Sum Linear Quadratic Games
Department of Electrical and Computer Engineering & Coordinated Science Laboratory, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校电子工程与协调科学实验室部门）；Department of Operations Research and Financial Engineering, Princeton University（普林斯顿大学运筹学与金融工程系）
