Thursday, March 18, 2010

Game Theory

I finished my re-read of I'm a Stranger Here Myself and I'm on to a new book: A Beautiful Math by Tom Siegfried.  It's about game theory, particularly John Forbes Nash's work (the mathematician who A Beautiful Mind was written about, hence the title).  I don't know much at all about game theory.  It's one of those things I heard math majors talk about in college but never actually found out what it was.  At some point I established that the "game" in game theory doesn't have anything to do with actual games.

Turns out I was wrong about that, that one thing I knew prior to starting the book.  It's mostly an economic theory, used for predicting how people (and other systems, it turns out) will behave.  It was developed by looking at simple, specific situations with clearly defined rules - things like a game of chess or checkers.

Here's one neat thing I learned so far: If I like A more than B, and I like B more than C, it follows that I like A more than C.  But how much more? How can you quantify how much you prefer one thing over another? John Von Neumann and Oskar Morgenstern (mathematicians in the first half of the 20th century) determined a way to do this.

The example the book uses involves Let's Make a Deal (statisticians love examples involving Monty Hall, I've learned that, too).  You're given a choice between a BMW, a new TV, and an old tricycle.  Let's assume you want the car.  You're told you can either have the TV, or you can have a 50% shot at the BMW.  Maybe you pick the TV.  Well, what if it was a 60% chance of getting the car? 70%?  The method is to find at what point you would decide to choose the chance at the BMW over the sure thing of the TV.  That percentage is a measure of how much more you prefer the BMW to the TV.  Cool!

I feel like rating tons of stuff like that now.  If I can get a new pair of earrings or a 50% chance of having a sheep live next door that I could go visit... Hmm....

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