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An Introduction to Game Theory An Introduction to Game Theory

07-16-2011 , 02:54 PM
When I'm bored I will be adding posts to this thread which define and illustrate basic concepts of game theory. With some basic definitions provided hopefully threads discussing game theory can avoid the pitfalls that happen over and over again when uninformed users choose to chime in.

If I can, I'll try to edit the first post to include direct links to my later posts, but if I am unable to it would be great if a mod could.

Pt1: Definition of a Game

Last edited by ArBar; 07-16-2011 at 03:00 PM.
An Introduction to Game Theory Quote
07-16-2011 , 02:58 PM
Game Theory Pt1: Definition of a Game

Generally speaking in game theory a game is a way of modeling interactions between agents when each agentís utility depends on their own decisions as well as the decisions of other agents. More formally to define a game you need to know:

1. The Players

Who the players are in the game is self-explanatory. You can label the players whoever you want: i.e. players 1,2,Ö,N; players A, B, C; Players Jack and Jill; etc. When naming players you should be careful about the use of N or 0. Typically these are reserved for representing nature, which is a special type of player in a game. Nature really doesnít play the game, but it instead determines things like who goes first, what type of player you are, etc based on some probability distribution.

2. The Rules of the Game

The rules of the game tell you when each player moves, what actions they are able to take at each move, what information is available to them at each move.

3. The Payoffs

Generally there is a fourth category in addition to players, rules, and payoffs: outcomes. However, Iím opting to lump outcomes under the payoffs category. The outcomes of the game are a function of the players actions, and a payoff is assigned to each possible outcome for each non-nature player.


With these basic definitions you should now know the basics of what a game is, so letís look at a well-known example.

There are two friends who want to meet in their small hometown which has one stoplight and only 2 alcohol serving establishments. Unfortunately both of them have lost their cellphones, laptops, and any other means of talking to each other. They had been planning to meet this evening for drinks but have not yet chosen where to go. Each friend must decide one establishment to go to, and if they meet up they can catch up and have fun which is valued at $10 than if they miss each other and have to drink alone which is valued at $0.

Who are the players?
Spoiler:
Friend 1 and Friend 2

What are the rules?
Spoiler:
The players are unable to communicate and have to decide where to meet for drinks.

What are the players actions?
Spoiler:
Go to establishment 1 or establishment 2

What are the outcomes?
Spoiler:
They arrive at the same establishment or they miss each other by going to different establishments

What are the payoffs?
Spoiler:
If they arrive at the same place, $10. If they miss each other, $0.
An Introduction to Game Theory Quote

      
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