I just saw the film, and the one question I have is, in the scene at the bar where Nash supposedly gets his brilliant idea for governing dynamics, is the solution he proposes really related to Nash equilibria? Every player in that situation would have something to gain by changing his strategy; even one of Nash’s friends said something to that effect. It just seemed like one of the oversimplified Numb3rs explanations of math.
By the way, as a Princeton student, it was very amusing to see familiar places on campus transformed into semi-hallowed scenes. That place where the pen ceremony takes place? That’s the entrance to the dining hall.
Taking any part of that movie seriously is a waste of time. Ron Howard, the director, so compromised any of the actual history of Nash as depicted in the original book that the movie should be named something completely different or at least have something like “inspired by” in the credits.
You can do a search to find threads that speak to the liberties taken back when it first came out. I am all for making sure that a movie is entertaining first, but to claim that this fiction is about a real person is a joke.
And to actually answer the question: no, the scenario with the girls in the movie does not represent a Nash equilibrium. At a Nash Equilibrium, it doesn’t benefit anyone to unilaterally change their decision. How does the scenario with the girls fail? For exactly the reason pointed out in the movie: if any one of the young men decide to go and get the blonde instead of the less hot friends, then he will get to be frisky with her instead of her friends. Oops.
Here’s an example of an actual equilibrium: We need to decide which side of the sidewalk to pass each other on. If we both move to our right, we pass without trouble. Likewise if we both move to our left. If we move one of each then we’re in trouble and neither of us can pass. So the equilibria are when we cooperate: if either of us changes our mind we’ll screw up the situation.
No worries. It looks a lot harsher in black and white than it did when I was typing it. There should probably be a little yellow happy face in there somewhere.
The essence of the Nash equilibrium is that all the players are happy with their decisions. That is, by changing their strategy they don’t help themselves. So with the passing a stranger example if we both move to our right side, we each get a worse outcome by switching our choice. (That is, the outcome is bad if I change my choice. Not both of us. That’s the unilateral part.)
Ok, the computer is being confiscated. I’ll try to come back later.
