Distributed online path-length-independent algorithm for noncooperative games over unbalanced digraphs☆

This paper studies online noncooperative games with dynamic regrets. Existing online noncooperative games rely on the sublinear growth of the path-length of Nash equilibrium sequences when considering dynamic regrets, which implies that their cost functions cannot be rapidly time-varying. Moreover, most of related results depend on undirected communication graphs. However, in many engineering practices, the cost functions may change greatly over time and the communication graphs may be directed. Here our problem involves rapidly time-varying cost functions, i.e., the path-length of Nash equilibrium sequences at least linearly grows, and the interaction topologies are unbalanced digraphs. In order to make decisions online without regrets, we develop a distributed algorithm based on multi-step mirror descents. Under the algorithm, sublinear dynamic regret bounds are established. More importantly, the dynamic regrets are independent of the path-length of Nash equilibrium sequences, compared with existing results. Finally, the simulation results validate the effectiveness of our algorithm, and demonstrate that our algorithm has better performance than other related algorithms. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.