To play cat and mouse is for somebody or something to chase the other in a very strategic, teasing, and game-like way (like a cat chasing and playing with a mouse).

玩猫捉老鼠的游戏，是指某人或某事用战略性的手段挑衅和追逐着其他人(就像猫在追老鼠)。

youdao

Mr Huntsman seems quite relaxed on the hustings, taking up an impromptu pool game at a veterans' club, for example (he lost), and teasing the locals about their accents.

亨茨曼对这次竞选活动表现的很轻松。例如，他在老兵俱乐部即兴来了场撞球比赛(他输了)，还和当地人一起打趣他们的口音。

youdao

Rather, they keep talking about getting into the hardware game, teasing anything from a new console, to a redesign of the mouse and keyboard, to even a virtual reality headset which we saw them show recently.

FORBES: Connect