Game Theory

COMPETITION:
Its a watch word of modern life.A competitive situation is called a game.
The term game represents the conflict between two or more parties.
STRATEGY:
It is defined as a complete set of plans of action.Its a decision rule for making a choice fom the list of course of action.
Two types of Strategy:
1. Pure Strategy
2. Mixed Strategy

A strategy is called pure if one knows in advance of the play that its certain to be adapted irrespective of the strategy the other player might choose.

The optimal strategy mixed for each player may be determined by assigning to each strategy its probability of being chosen.
ie., the probabilistic combination of available choices of strategy.

PAY OFF:
Pay off is the outcome of playing the game.If a Player 'A' has 'm' course of action and Player 'B' has 'n' course of action then the Pay off matrix may be constructed as

                      Player B
                      1          2          ........................ n
                1[ a11     a12         ................... ....a1n
Player A  2   a21    a22       ...........................a2n           -----> Out come of A
                .
                .
                .
                m    am1     am2   .........................amn]
----> Out come of B

TYPES OF GAME:
1. 2 Person Game
2. n Persons Game

ZERO SUM GAME:
Its one in which the sum of payment to all the competitors is zero for every possible outcome of game.

Sum of points won= sum of points lost

TWO PERSON ZERO SUM GAME:
Gain of one player=Loss of other player

A game with 2 players where the gain of one player equals to the loss of other.