Is it ever rational to co-operate?

[lemmingllama]

So now I will begin my debut into creating more philosophy threads so we can get life back into the poor and underused mako reactor. Situation time folks, this time I will explain it all in the situation

We are now watching two macho men, Angelo and Berto, who are macho motorcyclists out to impress the chicks. They decide to play a game of Chicken to see who is more macho and deserves the praise of their female companions. The game is simple. From opposite ends of a long straight road, they accelerate towards each other, with no helmets of course. They follow the white line fast and straight, getting closer to a head on crash. The one to veer first is chicken, being too afraid to keep on going. The best outcome to Angelo is for Berto to veer and Angelo to keep on motoring along happily, showing how macho he is. The same holds true for Berto if Angelo veers. The second best outcome is for both to veer at the last second, showing intelligence and machoism at the same time, but not beating the other. The other outcome, which could be seen as better than both veering, is if they crash head on, showing their machoism but also having some broken bikes and people. So apart from the risk of the crash, what is the problem? Rationality of course! Yes we are, counter-intuitively it is true, making Angelo and Berto rational individuals, as far as those who play this game.

Angelo reasons "Either Berto will chicken out or he won't. If I keep my nerve, he could chicken out before me. If he does, I win. But suppose he doesnt, then to chicken out would be the worst outcome for me since my machoism prefers a crash to such dishonor. So whatever Berto does, I should hold my nerve and keep on going" Berto reasons likewise. Reason tells both not to veer away, leaving one possible option: a crash. There is a better option for both, to veery away just before crashing. Why not do that? Because if Angelo reckons that is what Berto will do, he may as well drive on and win; but Berto reasons likewise, if thinking that Angelo will veer away.

Now another idea, what if they secretly promise each other that they will veer just in time? If Angelo is sure Berto will keep his promise, whhy should Angelo keep his? Macho men are ashamed of chickening but not lying! Of course, Angelo would be aware that Berto would also be thinking that he, Berto, need not keep his word. So a crash again seems inevitable if the players are rational.

tl;dr If you play chicken and think, it seems the best option is to always go and never veer. So is it rational to co-operate?

[† Mute point]

Rational people understand that playing Chicken is a terrible idea.