Normally, you can press Spacebar during the minigame and the game will just throw some dice behind the scenes and decide a winner.
I thought pressing space was essentially that character giving in. At least that's the way it appeared to work in the last beta version I played (I haven't played the final game, I'm still waiting for my physical box). Whenever I did it, in SP or coop, whichever character pressed space automatically lost the argument.
