Distributed Nash Equilibrium Seeking in Games With Partial Decision Information: A Survey

Nash equilibrium, as an essential strategic profile in game theory, is of both practical relevance and theoretical significance due to its wide penetration into various fields, such as smart grids, wireless communication networks, and networked mobile vehicles. In particular, distributed Nash equilibrium seeking strategies have recently attracted increasing attention because they show remarkable advantages in relaxing the requirement of a central node for information broadcasting or full observation of players' actions. This article aims to provide a survey of distributed Nash equilibrium seeking in games with partial decision information, in which players can only exchange information with their neighbors and their objective functions may explicitly depend on all players' actions. First, fundamental problem descriptions on distributed Nash equilibrium seeking are presented. Second, related results on distributed Nash equilibrium seeking in general multiplayer games, aggregative games, and multicluster games are reviewed, respectively, where representative continuous- and discrete-time methods are explained in detail. Third, two practical applications, including collaborative control for a network of mobile sensors and energy consumption control in smart grids, are provided to demonstrate the applicability of distributed Nash equilibrium seeking strategies. Finally, some promising directions are suggested for future research.