cat and mouse

noun

1. 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.
2. Western U.S. tick-tack-toe(def 1).

Idioms

3. 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,
   1. to toy or trifle with.
   2. to use strategy on one’s opponent, especially while waiting to strike: The detective played cat and mouse with the suspect.