Also called cat and rat. a children's game in which players in a circle keep a player from moving into or out of the circle and permit a second player to move into or out of the circle to escape the pursuing first player.
play cat and mouse, to engage in a gamelike relationship in which evasion and pursuit are used:
They played cat and mouse for a while before she consented to go out with him.
4.
play cat and mouse with,
to toy or trifle with.
to use strategy on one's opponent, especially while waiting to strike:
The detective played cat and mouse with the suspect.
Origin
1910-15
Idioms and Phrases with play cat and mouse
play cat and mouse
Amuse oneself or trifle with, toy with, as in She loved to play cat and mouse with an admirer, acting by turns friendly, indifferent, and jealous. The analogy of a cat toying with a helpless mouse was drawn centuries earlier, but the precise term dates only from the early 1900s.