From Longman Dictionary of Contemporary Englishplay (a game of) cat and mouse (with somebody)play (a game of) cat and mouse (with somebody)PREVENTto pretend to allow someone to do or have what they want, and then to stop them from doing or having it The police played an elaborate game of cat and mouse to trap him. → cat
Examples from the Corpus
play (a game of) cat and mouse (with somebody)• They played cat and mouse with the Bay, now scrambling for the outside, now sneaking back in.• For the rest of the hunting season, the saboteurs will play a cat and mouse game with the huntsmen. 