# ML Wiki

## 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 $P_2$
• 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: