Method

algebraic method Steps (Rule)
Step-1:	A play's (`p_1`, `p_2`) `p_1=(d - c)/((a + d) - (b + c))` and `p_2 = 1 - p_1`
Step-2:	B play's (`q_1`, `q_2`) `q_1=(d - b)/((a + d) - (b + c))` and `q_2 = 1 - q_1`
Step-3:	Value of the game `V` `V=(a * d - b * c)/((a + d) - (b + c))`

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Example-1
1. Find Solution of game theory problem using algebraic method

Player A\Player B	B1	B2
A1	1	7
A2	6	2

Solution:
1. Saddle point testing
Players

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

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

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

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Matrix size is 2`xx`2, so dominance rule is not required.

Solution using algebraic method
Here `a=1,b=7,c=6,d=2`

`p_1=(d - c)/((a + d) - (b + c))=(2 -6)/((1 +2) - (7 +6))=(-4)/(3 -13)=2/5`

`p_2=1-p_1=1-2/5=3/5`

`q_1=(d - b)/((a + d) - (b + c))=(2 -7)/((1 +2) - (7 +6))=(-5)/(3 -13)=1/2`

`q_2=1-q_1=1-1/2=1/2`

`V=(a * d - b * c)/((a + d) - (b + c))=((1 xx 2) - (7 xx 6))/((1 +2) - (7 +6))=(2 -42)/(3 -13)=4`

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