Online Learning Algorithm for Multi-agent Noncooperative Games

This paper explores online noncooperative games (NGs) with constrained involving multi-agent systems on unbalanced directed graphs (digraphs), where players try to minimize their objective functions selfishly, and the objective functions and decisions of it are vary with time. Additionally, the players are bound to time-varying constraints. To seek the stable sequence of the game online, that is the generalized Nash equilibrium (GNE) sequence, we developed a distributed online learning algorithm, which utilizing primal-dual, gradient descent, and projection methods. This approach achieved sublinear bounded dynamic regrets and constraint violations. Ultimately, the example of online electricity market games demonstrates the effectiveness of the introduced algorithm.