Danny
2004-05-25 17:37:50 |
A Beautiful Mind
This movie was on last night and I just wanted to run something by the smartest people I know. I noticed when Nash came up with the idea for his thesis in the bar it was all wrong. For those of you that haven't seen it...
Nash is with 3 other guys when 5 women walk into the bar. 4 of them are average looking and the other is really beautiful. He says that if all four of them tried to pick up the beautiful one then they will just get in each others way and she will choose none of them. Then if they tried to pick up the other four women separately they will all give them the cold shoulder because no girl likes to be second choice. But if they all ignored the beautiful woman then they all could end up with someone. My point is, that don't you think the best outcome would've been for one of the guys to end up with the beautiful one? If he would've convinced the other guys to ignore the beautiful one (like he did), but in his mind know that after the 3 other guys pick one of the average looking girls then he would have been left with the choice of one of the average looking girls and the beautiful one. After being passed up by 3 guys I don't think she would have turned him down. Sneaky, right? But that would've been the best outcome. IMHO.
PS: Who do you think is smarter, John Nash or Will Hunting? |
SilverKnight
2004-05-25 17:54:05 |
Re: A Beautiful Mind
For plot purposes and entertainment value (particularly for those who are not of a mathematical bent), they could not go over the subtleties of the thesis. But one underlying assumption to his model is that everyone acts in a "similar", if not identical manner.
So, to follow your line of reasoning, all 4 "gentlemen" would be agreeing to this, each thinking the other three are going after other women, and they'd all go after the beautiful one resulting in the first situation.
It actually isn't that far removed from the "prisoner's dilemma" and other game theory problems involving "best" decisions based on (perhaps) limited information and other players choices/responses. |
