As soon as he said "she was the only one who understood the game," I wondered whether he really understood the game, broadly construed.

Especially if we imagine some reasonable distribution of other players' actions, breaking from cooperation only benefits the player when 1) you bid the highest and therefore receive the money, or 2) everybody (or a majority) breaks cooperation and you don't look bad for doing so.

Even then, 1) is only good if the money outweighs the social costs. Heck, there might be future financial costs, if they play cooperation games in the future in that class!