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### Game Theory and Payoff Matrices

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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>
```
Associated Topics:
High School Logic
High School Probability

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