Provable Sample Complexity Guarantees for Learning of Continuous-Action Graphical Games with Nonparametric Utilities

Game theory has been extensively used as a framework to model and study the strategic interactions amongst rational but selfish individual players who are trying to maximize their payoffs. Game theory has been applied in many fields including but not limited to social and political science, economics, communication, system design and computer science. In non-cooperative games each player decides its action based on the actions of others players. These games are characterized by the equilibrium solution concept such as Nash equilibrium (NE) [18] which serves a descriptive role of the stable outcome of the overall behavior of self-interested players (e.g., people, companies, governments, groups or autonomous systems) interacting strategically with each other in distributed settings. Graphical games, introduced within the AI community about two decades ago, graphical games [16], are a representation of multiplayer games which capture and exploit locality or sparsity of direct influences. They are most appropriate for large-scale population games in which the payoffs of each player are determined by the actions of only a small number of other players. Indeed, graphical games played a prominent role in establishing the computational complexity of computing NE in normal-form games as well as in succinctly representable multiplayer games (see, e.g., [5, 6, 7] and the references therein). Graphical games have been studied for both discrete and continuous actions.