Optimal strategy analysis for adversarial differential games

Optimal decision-making and winning-regions analysis in adversarial differential games are challenging theoretical problems because of the complex interactions between players. To solve these problems, we present an organized review for pursuit-evasion games, reach-avoid games and capture-the-flag games; we also outline recent developments in three types of games. First, we summarize recent results for pursuit-evasion games and classify them according to different numbers of players. As a special kind of pursuit-evasion games, target-attacker-defender games with an active target are analyzed from the perspectives of different speed ratios for players. Second, the related works for reach-avoid games and capture-the-flag games are compared in terms of analytical methods and geometric methods, respectively. These methods have different effects on the barriers and optimal strategy analysis between players. Future directions for the pursuit-evasion games, reach-avoid games, capture-the-flag games and their applications are discussed in the end.