GTT

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

		Player 2
		A (q)		B (1-q)
Player 1	A (p)	1	-3	6	-6
Player 1	B (1-p)	2	-6	-6	-4

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

\begin{equation} EV_{2}(A) = -3p + -6(1-p) = 3p -6 \\\ EV_{2}(B) = -6p + -4(1-p) = -2p -4 \\\ 3p -6 = -2p -4 \\\ 5p= 2 \\\ p = \frac{ 2 }{ 5 } = 0.4 \\\ \\\ EV_{1}(A) = 1q + 6(1-q) = -5q + 6 \\\ EV_{1}(B) = 2q + -6(1-q) = 8q -6 \\\ -5q + 6 = 8q -6\\\ -13q= -12 \\\ q = \frac{ -12 }{ -13 } = 0.92 \\\ \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).