That's not a zero-sum game, though. The total money awarded to both players isn't the same in all outcomes. That's the whole reason why the game isn't purely ad

That's not a zero-sum game, though. The total money awarded to both players isn't the same in all outcomes. That's the whole reason why the game isn't purely adversarial and it makes sense to negotiate. I remember seeing this clip in 2012, and back then I proposed a solution based on correlated equilibria which still seems pretty good to me: "We have two minutes to talk, right? I'm going to ask you to flip a coin (visibly to both of us) at the last possible moment, the exact second where we must cease talking. If the coin comes up heads, I promise I'll cooperate, you can just go ahead and claim the whole prize. If the coin comes up tails, I promise I'll defect. Please cooperate in this case, because you have nothing to gain by defecting, and anyway the arrangement is fair, isn't it?"