Alexa and Judd have been dating for a year, and they are serious. On a beautiful summer weekend, both decide to go out. However, they have differences of opinion in choosing the place to meet, and no way of discussing the issue before their meeting. They have two options:Movie and Dinner.If both go to dinner, then Judd's payoff is 13 and Alexa gets 9. If both choose to go to movie, then each of them gets a payoff of 10. If Alexa goes to dinner alone, then Alexa gets a payoff of 13. If Judd goes to dinner alone, then Judd gets a payoff of 9. If both choose to go to movie alone, then each gets a payoff of 11.

Probability of Judd choosing his pure strategyDinner:

a.

2/5

b.

3/5

c.

1/5

d.

4/5

e.

2/3

Probability of Alexa choosing her pure strategyDinner:

a.

1/3

b.

2/3

c.

2/5

d.

1/5

e.

3/5

UniqueMixed Strategy Nash Equilibrium for this game:

a.

(2/3, 2/5)

b.

(1/3, 3/4)

c.

(3/5, 3/4)

d.

(2/3, 1/5)

e.

(1/5, 2/5)

For this particular question, there might be a difference between options below and your answer due to different decimal points in your calculator. Choose the optionclosestto your answer.

Expected payoff of Alexa from choosing her pure strategyMovie:

a.

10.6

b.

20.6

c.

15.6

d.

5.6

e.

6.6

For this particular question, there might be a difference between options below and your answer due to different decimal points in your calculator. Choose the optionclosestto your answer.

Expected payoff of Judd from choosing his pure strategyMovie:

a.

20.33

b.

15.33

c.

10.33

d.

5.33

e.

3.33

Now the story changes a bit! Because Alexa started liking Judd's friend Bob, Judd breaks up with Alexa and starts dating Jasmine's friend Lilly.

Assume that Lilly gets a payoff of 12 when both (Lilly and Judd) choose to go to amovie.What is the best-reply for Judd when Lilly's probability of choosing her pure strategymovieis less than 2/3?

Rest other payoffs for the remaining strategies remain the same as per the previous story of Alexa and Judd. Lilly is replacing Alexa with a new payoff for Lilly choosing her pure strategy movie when Judd chooses movie.

a.

Dinner

b.

Movie

c.

Dinner and Movie

d.

Start dating Jasmine

e.

None of the options