Solve the following game by graphical method.
Problem
Solve the following game by
graphical method.
Solution First consider the row minima
Next, consider the column maxima
We see that Maximum { row minima}
≠ Minimum { column maxima } So, the game has no saddle point.
It is a mixed game. Let p be the probability that
player A will use his first strategy. Then the probability that A will
use his second strategy is 1-p. When B uses his first strategyThe
expected value of pay-off to player A is given by
When B
uses his second strategy The expected value of pay-off to
player A is given by
Consider equations (1) and (2). For plotting the two equations on a
graph sheet, get some points on them as follows:
Graphical
solution Take probability and expected value along two rectangular axes in a
graph sheet. Draw two straight lines given by the two equations (1) and (2). Determine the point of intersection of the two straight lines in
the graph. This will provide the common solution of the two equations (1) and (2). Thus
we would get the value of the game.
Represent the two equations by the two straight lines
AB and CD on the graph sheet. Take the point of intersection of AB and CD as T.
For this point, we have p = 1/3 and E = -2. Therefore, the value V of the game is -2.
Tags : Operations Management - Game Theory, Goal Programming & Queuing Theory
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