Method

saddle point Steps (Rule)
Step-1:	1. Select the minimum element from each row and write them in Row Minimum column. 2. Select the maximum element from Row Minimum column and enclose it in [ ]. It is called Row MaxiMin.
Step-2:	1. Select the maximum element from each column and write them in Column Maximum row. 2. Select the minimum element from Column Maximum row and enclose it in ( ). It is called Column MiniMax.
Step-3:	1. Find out the elements that is same in rectangle [ ] and circle ( ). 2. If Column MiniMax = Row MaxiMin then the game has saddle point and it is the value of the game.

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Example-1
1. Find Solution of game theory problem using saddle point

Player A\Player B	B1	B2	B3	B4
A1	20	15	12	35
A2	25	14	8	10
A3	40	2	10	5
A4	-5	4	11	0

Solution:
1. Saddle point testing
Players

			Player `B`
			`B_1`	`B_2`	`B_3`	`B_4`
Player `A`	`A_1`		20	15	12	35
	`A_2`		25	14	8	10
	`A_3`		40	2	10	5
	`A_4`		-5	4	11	0

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

			Player `B`
			`B_1`	`B_2`	`B_3`	`B_4`		Row Minimum
Player `A`	`A_1`		20	15	[(12)]	35		`[12]`
	`A_2`		25	14	8	10		`8`
	`A_3`		40	2	10	5		`2`
	`A_4`		-5	4	11	0		`-5`
	Column Maximum		`40`	`15`	`(12)`	`35`

Select minimum from the maximum of columns
Column MiniMax = (12)

Select maximum from the minimum of rows
Row MaxiMin = [12]

Here, Column MiniMax = Row MaxiMin = 12
`:.` This game has a saddle point and value of the game is 12


The optimal strategies for both players are
The player A will always adopt strategy 1
The player B will always adopt strategy 3

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