In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN) channel, and (2) asynchronous data transmission via a fixed scheduling policy. Since the complexity of solving the game increases with the number of agents, we use the Mean-Field Game paradigm to solve it. Under standard assumptions on the information structure of the agents, we prove that the control of the agent in the MFG setting is free of the dual effect. This allows us to obtain an equilibrium control policy for the generic agent, which is a function of only the local observation of the agent. Furthermore, the equilibrium mean-field trajectory is shown to follow linear dynamics, hence making it computable. We show that in the finite population game, the equilibrium control policy prescribed by the MFG analysis constitutes an $ε$-Nash equilibrium, where $ε$ tends to zero as the number of agents goes to infinity. The paper is concluded with simulations demonstrating the performance of the equilibrium control policy.
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）
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）
