In Game Theory the decision of a decision maker and its consequences are based on somebody else's decisions

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

There are many types of games:

- Normal Form Game (also Strategic Game)
- Extensive Form Game
- Mixed-Strategy Game
- Repeated Game
- Coalitional Game
- Bayesian Game

It is often assumed that agents behave rationally:

- a
*rational agent*wants to maximize the consequence (utility, etc) - There are some important principles:
- The Dominance principle (same as Unanimity) Iterative Removal
- Nash Equilibrium

Paradoxes

- Matching Pennies (also "Head or Tail" game)

General Games

Other

- Cournot Duopoly Model
- Bertrand Duopoly Model
- Median Voter Theorem (also known as the Allocation Problem)