GAME THEORY

I was looking through a Barnes and Noble science section for a book on quantum theory (DON'T JUDGE), and I found a book entitled "Game Theory". I began to look through it and found it to be very interesting. Although I didn't find a good (and easy to understand) book on QT, I almost got the Game Theory.

In game theory, only two things define a game-
-there are two or more players...
-who interact to maximize a 'Utility'.

In games, Utility are the 'points'-- or, if no points, a numerical representation of the situation they're in. Usually it's an estimate.

Let's give an example.
There are two prisoners A and B. Together, they committed a crime for which they could get 10 years in prison. However, they are each offered a deal in which they can confess and testify against their partner (defect) or refuse to admit it (refuses). This is the deal to both of them:
a) If you defect and your friend refuses, you escape free and your friend gets 20 years.
b) If you both defect, you both get 5 years.
c) If you both refuse, you get 10 years.

Let's analyze!
If your friend will defect, your best option is to defect too, because it reduces your sentence by 15 years. However, if your friend will likely refuse, you should defect, as it will reduce your sentence by 10 years. Your best option is to defect, because the average between your possible sentences will reduce by 7.5 years than if you refuse. Think of it this way-

This is called a matrix, if you don't know. But I'm assuming that you do.

We could also plot it on a tree.

An interesting property of the PD is that the players technically do not interact-- it's what they do when they don't interact that makes it an interesting game.

There's a concept called Nash Equilibrium that's relatively important to game theory. From what I can tell, it's a situation where no players want to change their strategy. In a way, it means that they won't gain anything by changing their strategy.
A NE in Prisoner's Dilemma is, let's say, both players choose to defect. If either player decides to change their strategy, they'll lose.

There's also another game called Morra that you may have played. This is an interesting game that is played like rock-paper-scissors.
In Morra, only two players compete. So, on the count of whatever, each player holds up a number on their fingers from one to ten. If the sum of their numbers is even, one player wins; and vice versa.
Here's a chart I created-

Notice that the number they pick doesn't matter-– only if it's even or odd does.The odd player should do the opposite of the even player, but the even player should do the same as the odd. There is no real 'better strategy', unless you somehow read your opponent's mind, or predict the future.

Anyway, I guess that's it! There are tons of other good games-- Rock Paper Scissors, Nim, 2/3 the Average, and Fair Division (Cake Cutting). You acan look at them if you want.

Stay coolio, John

*PS: Sorry if this was a bad post-- Game Theory is extremely general*