**Game theory** was developed for the purpose of analyzing competitive
situations involving conflicting interests. In other words, game theory
is used for decision making under conflicting situations where there
are one or more opponents (i.e., players).

For example, chess, poker,
etc., are the games which have the characteristics of a competition
and are played according to definite rules. Game theory provides solutions
to such games, assuming that each of the players wants to maximize his
profits and minimize his losses.

How to select the optimal strategy without knowledge of the competitors is the basic problem of playing a game?

The *game theory* models can be classified into several categories. Some
important categories are listed below.

**Two-person & N-person games**

If the number of players
is two, it is known as two-person game. On the other hand, if the
number of players is N, it is known as N-person game.

**Zero sum & Non-zero sum game**

In a zero sum game, the
sum of the points won equals the sum of the points lost, i.e., one
player wins at the expense of the other. To the contrary, if the sum
of gains or losses is not equal to zero, it is either positive or
negative, then it is known as non-zero sum game. An example of non-zero
sum game is the case of two competing firms each with a choice regarding
its advertising campaign. In such a situation, both the firms may
gain or loose, though their gain or loss may not be equal.

**Games of Perfect and Imperfect information**

If the strategy
of a player can be discovered by his competitor, then it is known
as a perfect information game. In case of imperfect information games
no player has complete information and tries to guess the real situation.

**Pure & Mixed strategy games**

If the players select the
same strategy each time, then it is referred to as pure strategy games.
If a player decides to choose a course of action for each play in
accordance with some particularly probability distribution, it is
called mixed strategy game.

## Assumptions of Game Theory

- There are finite number of competitors (players).
- The players act reasonably.
- Every player strives to maximize gains and minimize losses.
- Each player has finite number of possible courses of action.
- The choices are assumed to be made simultaneously, so that no player
knows his opponent's choice until he has decided his own course of
action.
- The pay-off is fixed and predetermined.
- The pay-offs must represent utilities.