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Player `B`

Player `A`

Player `A`

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Solution

Problem: Matrix method of Game Theory {{1,7,2},{6,2,7},{5,1,6}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Matrix method of Game Theory {{1,7,2},{6,2,7},{5,1,6}}

1. Saddle point testing
Players

		Player `B`
		`B_1`	`B_2`	`B_3`
Player `A`	`A_1`	1	7	2
	`A_2`	6	2	7
	`A_3`	5	1	6

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

		Player `B`
		`B_1`	`B_2`	`B_3`	Row Minimum
Player `A`	`A_1`	1	7	2	`1`
	`A_2`	(6)	[2]	7	`[2]`
	`A_3`	5	1	6	`1`
	Column Maximum	`(6)`	`7`	`7`

Select minimum from the maximum of columns
Column MiniMax = (6)

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

Here, Column MiniMax `!=` Row MaxiMin

`:.` This game has no saddle point.

2. Dominance rule to reduce the size of the payoff matrix
Using dominance property

		Player `B`
		`B_1`	`B_2`	`B_3`
Player `A`	`A_1`	1	7	2
	`A_2`	6	2	7
	`A_3`	5	1	6

row-3 is dominated by row-2 (row-3 `<=` row-2), so row-3 is deleted, `(A_3 <= A_2 : 5<=6,1<=2,6<=7)`

		Player `B`
		`B_1`	`B_2`	`B_3`
Player `A`	`A_1`	1	7	2
Player `A`	`A_2`	6	2	7

column-3 is dominated by column-1 (column-3 `>=` column-1), so column-3 is deleted. `(B_3 >= B_1 : 2>=1,7>=6)`

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