Find Solution of game theory problem using Bimatrix method

Player A\Player B	L	R
U	2,-3	1,2
D	1,1	4,-1

Solution:

			Player `B`
			`L`	`R`
Player `A`	`U`		2, -3	1, 2
	`D`		1, 1	4, -1

			Player `B`
			`color{green}{L}`	`color{green}{R}`
Player `A`	`color{red}{U}`		2 , -3	1 , 2
	`color{red}{D}`		1 , 1	4 , -1

The cells with both entries underlined represents pure strategy nash equilibrium.
The game has no pure strategy nash equilibrium

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Let p be the probability of Player-1 and q be probability of Player-2.
For Player-1
`E(U)=2*q+1*(1-q)`

`E(D)=1*q+4*(1-q)`

`E(U)=E(D)`

`=>2q+(1-q)=q+4(1-q)`

`=>4q=3`

`=>q=3/4`

`=>(1-q)=1-3/4=1/4`

For Player-2
`E(L)=-3*p+1*(1-p)`

`E(R)=2*p-1*(1-p)`

`E(L)=E(R)`

`=>-3p+(1-p)=2p-(1-p)`

`=>-7p=-2`

`=>p=2/7`

`=>(1-p)=1-2/7=5/7`

The payoff for player-1 is
`(2xx3/4)+(1xx1/4)=(1xx3/4)+(4xx1/4)=7/4`

The payoff for player-2 is
`(-3xx2/7)+(1xx5/7)=(2xx2/7)+(-1xx5/7)=-1/7`

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