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GRAPHICAL METHOD
Graphical methods can be used in games with no saddle points and having pay off m X 2 or 2 X n matrix.The aim is to substitute a much simpler 2 X 2 matrix for the original m X 2 or 2 X m matrix.
Example:Establish the optimum strategies and the value of the game from the following payoff matrix game.
Draw two vertical axes and plot two payoffs corresponding to each of the five columns. The pay off numbers in the first row is plotted on Axis I and those in second rows on Axis II.
Thus the two pay off numbers 6 and 3 in the first column are shown respectively by point A on Axis I and point B on Axis II.Join the corresponding pay off numbers on Axis I and Axis II by straight lines.On the two intersecting lines at the very bottom, thicken them from below up to the point of intersection, i.e. utmost point on the boundary.The thick lines on the graph KT and LT meet at T
The two lines passing through T, identify the two critical moves of Y which combined with X, yield the following 2 X 2 matrix.
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The assignment model Consider the situation of assigning m jobs (or workers) to n machines. A job i(= 1,2,3 ...m) when assigned to machine j(= 1,2,3 ...n) acquires a cost Cij.
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