to play cat and mouse is to try to defeat someone by tricking them into making a mistake so that you have an advantage over them (often + with )
Example: The 32-year-old actress spent a large proportion of the week playing cat and mouse with the press.
play (a game of) cat and mouse:
1. to repeatedly try to make someone react in a way that will cause them problems.
Example: Enemy warplanes have been playing a deadly game of cat and mouse, trying to bring the fighter planes into range of their missiles.
2. to try to find someone who is hiding from you.
Example: Hotel Security played cat and mouse with the teenagers trying to enter the hotel to see their favourite singer.
Etymology: based on the way a cat plays with a mouse before killing it.