a battle of wits

A competition in which opponents attempt to gain victory or an advantage over each other using their intelligence. The two young geniuses entered into a battle of wits as they competed for first place in the national trivia championship. As each candidate tried to defend his stance on the hot-button issue, a battle of wits began as they each produced seemingly endless lists of statistics to support their views. Yeah, this isn't a battle of wits against your opponents anymore—now, you have to convince the general population to vote for you.

a battle of wits

If a competition or disagreement is a battle of wits, each person involved in it uses their intelligence to beat their opponents. With chess you're involved in a battle of wits from start to finish.

a battle of ˈwits

a competition, an argument or a struggle where each side uses their ability to think quickly to try to win: It’s a battle of wits between the hero and the villain.