To set this up, here's a little movie clip from "A Beautiful Mind," which I watched last night on TBS.
And here is a transcript of what Nash says:
Adam Smith needs revision. If we all go for the blonde, we block each other. Not a single one of us is gonna get her. So, then we go for her friends. But they will all give us the cold shoulder because nobody likes to be second choice. But, what if no one goes for the blonde? We don't get in each other's way. And we don't insult the other girls. It's the only way we win. It's the only way we all get laid. Adam Smith said 'the best result comes from everyone in the group doing what's best for himself,' right? Incomplete, incomplete. Because the best result will come where everyone in the group [is] doing what's best for himself and the group. Governing dynamics. Adam Smith, gentlemen, is wrong.
Got that? It's not in our best interest to act in our own best interest. It's in our best interest to act in the group's best interest. That way, everybody wins. We all get what we want. Sounds a bit utopian, eh? Even socialist. Does that surprise you, coming out of Hollywood?
Unfortunately, the public at large never read Adam Smith or John Nash, and so most people get their education from the simplification offered to us by Hollywood. And Hollywood got it wrong. Which is a real bummer because they have the expertise and the tools to make the complicated easier to understand. I think Ron Howard did a great job using effects to explain the movie's version of Nash, except that Nash never believed what the movie told you.
Quick question: who is more valuable in the group of girls? The blonde or a brunette? The blonde. But because Nash explains in the movie that the blonde is unattainable by all of them, they can all settle for a brunette each, and get what they each truly want: a girl for the night. Everyone is happy, right?
Ever seen that played out in real life? Men are a bit competitive. One of them will go for the blonde just to edge out the other guys and prove himself.
Further, the Nash Equilibrium doesn't state what the movie says. From Wikipedia:
A solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy.
Let's go back to Nash's bar scene. If the blonde has higher value than the brunettes, and the guys all agree that they'll go for the brunettes, then the guy who patiently waits until each of the other guys has made his move on a brunette is the one who can get the blonde. Knowing the strategies of his fellow men, he of course would change his strategy and attain the higher value.
To Hollywood, I say, "Incomplete! Incomplete!"
Nash's theorem requires that if all of the players know the strategies of the other players, nothing would change. But in real life, amongst competing players and differing values, that doesn't play out. Hell, watch any episode of Survivor and you learn that. But of course, Survivor isn't scripted. It uses real people with real motives.