He smiled. She sniffed. He sat. She stalked. He called her a “puppet.” She called him a “nasty man.” These were the 2016 presidential debates as re-enacted in Greenwich Village over the weekend.

At the Provincetown Playhouse on Saturday, professors from New York University, the Rhode Island School of Design and the French business school Insead twice presented “Her Opponent,” a free 35-minute performance composed of excerpts from the three presidential debates with a significant twist in the casting: Donald J. Trump was played by a woman, Rachel Tuggle Whorton, a Ph.D. candidate and adjunct instructor at N.Y.U. Hillary Clinton was played by a man, Daryl Embry, another adjunct instructor. To complete the gender inversion, the candidates were given new names, Brenda King in place of Mr. Trump, Jonathan Gordon for Ms. Clinton.

Drawing on the techniques of documentary theater, as practiced by the likes of Anna Deavere Smith, these actors not only studied the words of the candidates but also the gestures, posture, tempo and vocal intonation that each used. As Andy Wagner, the actor playing the moderator explained, the creators wanted to see if gender-inverted casting would “cause people to revisit their own personal biases and develop insights or a different perspective.”