GTT

Find the Mixed strategy Nash equilibria (MSNE) of presented game

		Player 2
		A (q)		B (1-q)
Player 1	A (p)	-1	-6	-6	-5
Player 1	B (1-p)	2	-4	0	-1

You can click on the payoffs in the table to note down best responses of the players.

\begin{equation} EV_{2}(A) = -6p + -4(1-p) = -2p -4 \\\ EV_{2}(B) = -5p + -1(1-p) = -4p -1 \\\ -2p -4 = -4p -1 \\\ 2p= 3 \\\ p = \frac{ 3 }{ 2 } = 1.5 \\\ \\\ EV_{1}(A) = -1q + -6(1-q) = 5q -6 \\\ EV_{1}(B) = 2q + 0(1-q) = 2q + 0 \\\ 5q -6 = 2q + 0\\\ 3q= 6 \\\ q = \frac{ 6 }{ 3 } = 2.0 \\\ \end{equation}

Select one answer of the following:

There is no MSNE in this game.

There is no pure strategy NE but there is a MSNE in this game.

There is one pure strategy NE and there is a MSNE in this game.

There are two pure strategy NE and there is a MSNE in this game.

There are three pure strategy NE and there is a MSNE in this game.

If there is a MSNE in this game, it has probabilities of

[( , ); ( , )]

Enter your answer as a number rounded to two digits or a fraction (1/3 can be entered as 0.33 or 1/3).