Differential Games: A New Perspective with Artificial Intelligence

Differential Game Theory has seen significant advancements in recent years, driven by numerous scholars exploring theoretical and practical aspects of the field. In this paper, we summarize the principal findings in pursuit-evasion games, focusing on Cop-Win and Robber-Win games on graphs. A dedicated section explores the demonstration technique introduced by G. Ibragimov, showcasing how evasion or capture can be achieved in a chase game by defining time intervals. The paper concludes by presenting key open problems in this area, with a special emphasis on applying artificial intelligence to trajectory prediction.