Value of the game-game theory, Mathematics

Value Of The Game

The game value refers to the average pay off per play of the game over an extended period of time

                                                          1766_Value Of The Game.png

In this game player X will play his first/initial row on each play of the game. Player y will have to play first or initial column on each play of the game in order to minimize his looses hence this game is in favour of X and he wins 3 points on all play of the game.It is a game of pure strategy and the value of the game is 3 points in favour of X

Illustration

Find out the optimum strategies for the two players X and Y and determine the value of the game from the given pay off matrix:

                                                        140_Value Of The Game 1.png

Strategy suppose the worst and acts accordingly

If X plays first

If X plays first along with his row one then Y will play along with his 2nd column to win 1 point similarly if X plays along with his 2nd row then Y will play his 3rd column to win 7 points and if x plays along with his 3rd row then Y will play his fourth column to win 9 points

In this game X cannot win then he should adopt first row strategy in order to minimize losses

This decision rule is identified as 'maximum strategy' that is X chooses the highest of these minimum pay offs

By using the same reasoning from the point of view of y

X will play his 3rd row to win 4 points, If Y plays with his 1st column

X will play his 1st row to lose 1 point, If Y plays with his 2nd column

X will play his 1st row to win 4 points, If Y plays with his 3rd column

X will play his 1st row to win 2 points, If Y plays with his 4th column

Hence player Y will make the best of the situation by playing his 2nd column that is a 'Minimax strategy'

This type of game is also a game of pure strategy and the value of the game is -1 as win of 1 point per game to y by using matrix notation, the solution is displayed below:

                                                                              111_Value Of The Game 2.png

In this case the game value is -1

Minimum of the column maximums is -1

Maximum of the row is also is -1

That is X's strategy is maximim strategy

            Y's strategy is Minimax strategy

 

Posted Date: 2/19/2013 5:22:49 AM | Location : United States







Related Discussions:- Value of the game-game theory, Assignment Help, Ask Question on Value of the game-game theory, Get Answer, Expert's Help, Value of the game-game theory Discussions

Write discussion on Value of the game-game theory
Your posts are moderated
Related Questions

why zero factorial is equal to one


how do you do algebra in 4th grade

Find out a series solution for the following differential equation about x 0 = 0 y′′ + y = 0.   Solution Note that in this case p(x)=1 and therefore every point is an or

Describe Independent Events in maths? Events are independent if the outcome of one event does not affect the outcome of the second event. If A represents one independent event

First, see that the right hand side of equation (2) is a polynomial and thus continuous. This implies that this can only change sign if this firstly goes by zero. Therefore, if the

Find the magnitude of the following vectors: 5i+7j

how do you find the length of a parallel line connecting two external circles of different sizes from the outside, given the value of both radius and one parallel line.

Hi need a help for marketing strategic assignment Could you able to help me???