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."^[1] The "cat" is unable to secure a definitive victory over the "mouse", who despite not being able to defeat the cat, is himself too nimble to be caught. In extreme cases, the idiom may imply that the contest is never-ending.

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.

References

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2. see Cat and Mouse in 0g - a performance in a cosmonaut training plane in Russia by artist Lyn Hagan [www.lifeinspace.org]