Cat and mouse.

About Cat and mouse

Cat and mouse, often expressed as cat-and-mouse game, is an English-language idiom that means "a contrived action involving constant pursuit, near captures, and repeated escapes." The "cat" is unable to secure a definitive victory over the "mouse", who, despite not being able to defeat the cat, is able to avoid capture. In extreme cases, the idiom may imply that the contest is never-ending. The term is derived from the hunting behavior of domestic cats, which often appear to "play" with prey by releasing it after capture.