Cat and mouse

Cat and mouse, often expressed as cat-and-mouse game, is an English-language idiom dating back to 1675 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. This behavior is due to an instinctive imperative to ensure that the prey is weak enough to be killed without endangering the cat.

In colloquial usage it has often been generalized (or corrupted) to mean simply that the advantage constantly shifts between the contestants, leading to an impasse or de facto stalemate.