Game Theory problem using Saddle point Example-2

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Home > Operation Research calculators > Game Theory >> Saddle Point example

1. Saddle point example ( Enter your problem )

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2. Method & Example-1
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3. Example-2

Find Solution of game theory problem using saddle point
_{Player A}\^{Player B} B1 B2 B3
A1 -2 14 -2
A2 -5 -6 -4
A3 -6 20 -8

Solution:
1. Saddle point testing
Players

		Player `B`
		`B_1`	`B_2`	`B_3`
Player `A`	`A_1`	-2	14	-2
	`A_2`	-5	-6	-4
	`A_3`	-6	20	-8

We apply the maximin (minimax) principle to analyze the game.

		Player `B`
		`B_1`	`B_2`	`B_3`	Row Minimum
Player `A`	`A_1`	[(-2)]	14	-2	`[-2]`
	`A_2`	-5	-6	-4	`-6`
	`A_3`	-6	20	-8	`-8`
	Column Maximum	`(-2)`	`20`	`-2`

Select minimum from the maximum of columns
Column MiniMax = (-2)

Select maximum from the minimum of rows
Row MaxiMin = [-2]

Here, Column MiniMax = Row MaxiMin = -2
`:.` This game has a saddle point and value of the game is -2

The optimal strategies for both players are
The player A will always adopt strategy 1
The player B will always adopt strategy 1

This material is intended as a summary. Use your textbook for detail explanation.
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