1.nounA relationship in which two parties closely monitor and challenge one another in a suspicious or self-protective manner, often because each party is attempting to gain an advantage over the other.
"The Allied and the enemy submarine played a game of cat and mouse, checking up on each other's whereabouts and strategies."
2.nounA form of attack in which the attacker toys with the victim by inflicting minor damage or letting the victim have futile hopes of escape before finally finishing the victim off.
3.proper nounA children's game in which one player (the "cat") attempts to break through a ring of players to catch another player (the "mouse") in the centre.