Monday, April 7, 2008

the nash equilibrium

I just thought that since we would be watching a beautiful mind then we might as well as know why John Nash is important. He got his nobel prize, along with some colleagues for his work in game theory. He actually invented an entirely new way of looking at things.
In the Nash equilibrium, named after him of course, all the "players" of the "game" must think not only what is best for themselves, but also what is best for themselves in relation to the choices of the other "players."

Wikipedia uses this example
Stated simply, Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill's decision, and Bill is making the best decision he can, taking into account Amy's decision. Likewise, many players are in Nash equilibrium if each one is making the best decision that they can, taking into account the decisions of the others.

to me this idea doesn't really seem that new and amazing. i like to think of chess. One of the main faccets of the game is to see how your moves affect the moves of your opponent and then how that affects your moves and so on. the best players are actually always playing the game in the future, that is what the board will look like and not what it does.
But the Nash equilibrium won't really work with chess, because each player must know the others strategy to make their own decision, which definitely wouldn't help in a game like chess.

so that is the basics, probably poorly explained, of the Nash equilibrium. hopefully this helps just a bit and if not there is always Wiki to learn more.


Cheney said...

One example is in the movie where he describes the best way for him and his friends to get a girl at the bar. If they all go for the hot blonde they will block each other and no one will get her and then her less pretty friends will reject them not wanting to be a second choice. However if they all ignore the blonde and just go for the friends they all end up with a girl. By using a strategy that involves cooperation from all players they all get what they want in the end. Well except the hot blonde...

Blackout said...

game theory is still confusing.