Game Theory and Payoff Matrices

Date: 11/14/98 at 17:36:32
From: Anonymous
Subject: Game Theory (What it is and how it can be used)

I was assigned a rather difficult topic for my math honors term paper: 
game theory. After collecting several sources, I am baffled by what 
the authors of these game theory books are talking about. Can you help 
me? I would like to know what it is all about and how it can be used. 
I would also appreciate it if you could guide me to some Web sites 
that have information on this topic. Thanks!

Date: 11/14/98 at 20:23:08
From: Doctor Tom
Subject: Re: Game Theory (What it is and how it can be used)

Hi,

Try to find a copy of the book, "The Compleat Strategyst" by J. D. 
Williams in a library. It's a bit old, so it's probably out of print, 
but it's a great introduction to game theory.

Basically, the idea is to find optimal strategies for playing games.  
Here's an example. Suppose you and I are playing a game, and we can 
each choose 2 strategies - you can do A or B, and I can do C or D.  
Here's the payoff matrix:

       A    B
   C   5   -3
   D  -2    6

The number represents your payment to me, and if it's negative, it's 
my payment to you.

The "game" isn't fair to you, but if you have to play, what's your 
best strategy? Clearly since you must always choose A or B, I'll pick 
C if you're always playing A, and D if you always choose B. So your 
best strategy is to choose randomly between A and B, but with unequal 
probabilities. The purpose of game theory is to calculate those 
probabilities to minimize your losses (and the same is true for me - 
I can use it to find the same optimal mixed strategy to maximize my 
winnings.

Obviously most games have many more strategies, but as long as there's 
a payoff matrix as above, there is a unique best mixed strategy for 
each player. Game theory tells you how to get it.

- Doctor Tom, The Math Forum
  http://mathforum.org/dr.math/</a>