In a noncooperative dynamic game, multiple agents operating in a changing environment aim to optimize their utilities over an infinite time horizon. Time-varying environments allow to model more realistic scenarios (e.g., mobile devices equipped with batteries, wireless communications over a fading channel, etc.). However, solving a dynamic game is a difficult task that requires dealing with multiple coupled optimal control problems. We focus our analysis on a class of problems, named \textit{dynamic potential games}, whose solution can be found through a single multivariate optimal control problem. Our analysis generalizes previous studies by considering that the set of environment's states and the set of players' actions are constrained, as it is required by most of the applications. And the theoretical results are the natural extension of the analysis for static potential games. We apply the analysis and provide numerical methods to solve four key example problems, with different features each: energy demand control in a smart-grid network, network flow optimization in which the relays have bounded link capacity and limited battery life, uplink multiple access communication with users that have to optimize the use of their batteries, and two optimal scheduling games with nonstationary channels.
Distributed Equilibrium-Seeking in Target Coverage Games via Self-Configurable Networks under Limited Communication
Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫电气与计算机工程学院）；Department of Aerospace Engineering, University of Michigan（密歇根大学航空航天工程系）
Dynamic Multi-Robot Task Allocation under Uncertainty and Communication Constraints: A Game-Theoretic Approach
Department of Mechanical Engineering, University of California, Berkeley（加州大学伯克利分校机械工程系）；Department of Electrical Engineering and Computer Science, University of California, Berkeley（加州大学伯克利分校电气工程与计算机科学系）；Thayer School of Engineering, Dartmouth College（达特茅斯学院泰勒工程学院）
Fast Distributed Algorithm for Aggregative Games in Malicious Environment
Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education（华中科技大学图像处理与智能控制教育部重点实验室）
