Marie and Ana play a simultaneous one-shot game. Marie chooses between Top and Bottom, whereas Ana chooses between left and right. Payoffs are given by (Marie's payoffs are listed first and Ana's payoffs second):

Top+left: 12,2.

Top+right: 3,9.

Bottom+left: 5,8.

Bottom+right: 4,2.

1. What are the pure strategy Nash equilibria in this game?
2. In the mixed strategy Nash equilibria: (i) with what likelihood will Marie play top? (ii) What is the likelihood that Ana plays left? (iii) What are the expected utilities of Marie and Ana in the mixed strategy Nash equilibria?
3. Draw the best response functions for Marie and Ana.

Suppose the payoffs to each player are doubled, such that the new payoffs are given by (Marie's payoffs are listed first and Ana's payoffs second):

Top+left: 24,4.

Top+right: 6,18.

Bottom+left: 10,16.

Bottom+right: 8,4.

1. What is the mixed strategy Nash equilibria with the doubled payoffs? What are the expected utilities of Marie and Ana in the mixed strategy Nash equilibria?

Now, suppose the game is played sequentially, with Marie moving first and Ana going second.

1. What is the Nash equilibria of this sequential game?