Rules of game theory, Mathematics

Rules Of Game Theory

i.   The number of competitors is finite

ii.   There is conflict of interests among the participants

iii.  Each of these participants has available to him a finite set of obtainable courses of action that is choices

iv.  The rules governing these choices are known and identified to all players

      While playing each player chooses a course of action from a list of options available to him

v.  The outcome of the game is affected by options made by all of the players. The options are to be made simultaneously hence no competitor knows his opponents choice till he is already committed to his own

vi.   The outcome for all exact options by all the players is identified in advance and numerically defined

While a competitive situation meets all these criteria above we describe it a game

NOTE: only in a few real life competitive conditions can game theory be applied since all the rules are difficult to apply at the similar time to a described situation.

Illustration

Two players X and Y have two alternatives. They indicate their choices by pressing two types of buttons in front of them however they cannot see the opponents move. This is assumed that both players have equal intelligence and both intend to win the game.

This sort of simple game can be demonstration in tabular form as given below:

 

 

Player Y

 

 

Button R

Button t

Player X

Button m

X wins 2 points

X wins 3 points

 

Button n

Y wins 2 points

X wins 1 point

The game is biased against Y since if player X presses button m he will always win. Thus Y will be forced to press button r to cut/slice down his losses

Alternative illustration

 

Player Y

 

 

Button R

Button t

Player X

Button m

X wins 3 points

Y wins 4 points

 

Button n

Y wins 2 points

X wins 1 point

In such case X will not be capable to press button m all the time in order to win or button n. as same Y will not be capable to press button r or button t all the time in order to win. In such a condition each player will exercise his choice for part of the time based upon the probability

 

 

Posted Date: 2/19/2013 4:57:32 AM | Location : United States







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