Game Theory
In Game Theory the decision of a decision maker and its consequences are based on somebody else's decisions
Game
A game is a strategic interaction (in economics, social studies, networking, etc) between two or more self-interested agents
Each agent has his/her own opinions and preferences
The outcome of a game depends on what all agents do
- what actions a game player takes?
- all users act in the same way?
- is there a global behavior pattern?
- if players can communicate, what effect it will have?
- repetitions?
- does it matter if opponents are rational?
Example:
- Suppose we have two airline companies $P_1$ and $P_2$
- They are both thinking about about opening a new destination
- Both consider two options: either make tickets cheap or make them expensive
- Clearly if $p_1$ decides to sell cheap tickets while $p_2$ - to sell expensive tickets, everybody will buy from $p_1$
So we can depict it with the following pay-off matrix
- a cell represents consequences of the decision that both players take
$p_2 \leftarrow$
$p_1 \downarrow$ |
500 |
200
|
| 500
|
(50, 100) |
(-100, 200)
|
| 200
|
(150, -200) |
(-10, -10)
|
We see that:
- if both agree on cheap tickets - both will have profits
- if $p_2$ sells expensive tickets and $p_1$ cheap ones, all go to $p_1$ and $p_2$ will have losses
- the same with $p_1$ and $p_1$
- if both decide on expensive tickets - nobody will buy them and they both will experience losses
This is a variation of the Prisoner's Dilemma, an example of Normal Form Game
Types of Games
There are many types of games:
Rationality
It is often assumed that agents behave rationally:
Examples
Paradoxes
Pure Competition Games
Cooperation Games
General Games
Other
Sources