Game Theory

I’m taking two classes this fall, Econometrics, and Game Theory. Econometrics is basically applied statistics with respect to economic problems; it’s mostly very boring and our professor is not the best lecturer I’ve ever had. Frankly, I’ll be pleased once the course is over.
Game Theory though has proved a bit more interesting. One of the cool things that we learned about is what a Nash Equilibrium is, named after John Forbes Nash, the guy from Ron Howard’s ‘A Beautiful Mind’. And interestingly (but not surprisingly) the movie portrayed the idea incorrectly.
Here’s the basic premise. Suppose you’re playing a two player game. A Nash Equilibrium (NE) is a strategy for each player, and an outcome of that strategy, such that neither player could play a different strategy and do better, as long as his opponent played the same strategy. It would be a bit easier to explain on paper, but in simple terms all it says is that a game will calm down and everyone will be ‘content’, more or less, once all the individual opportunities for advancement have disappeared.
Simple enough, right? It’s actually a very powerful concept. The distressing thing is that the example the movie used is not a NE. The prettiest girl comes into the bar. She’ll refuse everyone if they approach her at once, and then none of the guys can get another girl, because nobody wants to be chosen second. So, they all have to ignore the pretty girl, so that they can all get a girl. However, the prettiest girl is still available, and under the premise that everyone would like to dance with her, somebody will, in effect, “cheat” and go ask her to dance. As long as she doesn’t have a partner, all the other guys are basically tempted to try and ‘do better’ by asking her.
It would have been easy to come up with a better example, and it’s irritating that Hollywood once again can’t seem to get certain technical details correct. But at least my class is interesting …