Find Solution of game theory problem using oddment method

Player A\Player B	B1	B2
A1	9	7
A2	5	11

Solution:
1. Saddle point testing
Players

			Player `B`
			`B_1`	`B_2`
Player `A`	`A_1`		9	7
	`A_2`		5	11

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

			Player `B`
			`B_1`	`B_2`		Row Minimum
Player `A`	`A_1`		(9)	[7]		`[7]`
	`A_2`		5	11		`5`
	Column Maximum		`(9)`	`11`

Select minimum from the maximum of columns
Column MiniMax = (9)

Select maximum from the minimum of rows
Row MaxiMin = [7]

Here, Column MiniMax `!=` Row MaxiMin

`:.` This game has no saddle point.

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

			Player `B`
			`B_1`	`B_2`
Player `A`	`A_1`		9	7
	`A_2`		5	11

Also, no course of action dominates the other

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Reduced matrix is

			Player `B`
			`B_1`	`B_2`
Player `A`	`A_1`		9	7
	`A_2`		5	11

Find oddments of individual strategies
1. Find absolute difference between the two values in the first row and put it against second row of the matrix
`|9-7|=2`

2. Find absolute difference between the two values in the second row and put it against first row of the matrix
`|5-11|=6`

3. Find absolute difference between the two values in the first column and put it against second column of the matrix
`|9-5|=4`

4. Find absolute difference between the two values in the second column and put it against first column of the matrix
`|7-11|=4`

So Oddment matrix is

			Player `B`
			`B_1`	`B_2`		Oddments
Player `A`	`A_1`		9	7		`|5-11|=6`
	`A_2`		5	11		`|9-7|=2`
	Oddments		`|7-11|=4`	`|9-5|=4`

Find probabilities of individual strategies
`P(A_1)=(6)/(2+6)=3/4`

`P(A_2)=(2)/(2+6)=1/4`


`P(B_1)=(4)/(4+4)=1/2`

`P(B_2)=(4)/(4+4)=1/2`


Value of game `V=(9*6+5*2)/(2+6)=64/8=8`

Value of game `V=(7*6+11*2)/(2+6)=64/8=8`

Value of game `V=(9*4+7*4)/(4+4)=64/8=8`

Value of game `V=(5*4+11*4)/(4+4)=64/8=8`

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