GTT

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

		Player 2
		A (q)		B (1-q)
Player 1	A (p)	-5	12	-6	13
Player 1	B (1-p)	-6	1	-5	-4

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

\begin{equation} EV_{2}(A) = 12p + 1(1-p) = 11p + 1 \\\ EV_{2}(B) = 13p + -4(1-p) = 17p -4 \\\ 11p + 1 = 17p -4 \\\ -6p= -5 \\\ p = \frac{ -5 }{ -6 } = 0.83 \\\ \\\ EV_{1}(A) = -5q + -6(1-q) = 1q -6 \\\ EV_{1}(B) = -6q + -5(1-q) = -1q -5 \\\ 1q -6 = -1q -5\\\ 2q= 1 \\\ q = \frac{ 1 }{ 2 } = 0.5 \\\ \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).