In pursuit-evasion games, one player (the pursuer) tries to catch the other (the evader). The evader tries to avoid capture. These games model scenarios like network security (attacker vs defender) or robotics (robot pursuing a target). The state is (pursuer position, evader position). The analysis is similar to Cat and Mouse but with different win conditions and move rules.
Each turn, one player moves first, then the opponent responds. The graph topology determines who has the advantage. On trees, the cop can trap the robber by cutting off escape paths systematically.