Dan tells her two daughters Brooke and Cassidi to pick a movie for their movie night.Brooke is very into classic horror movies and wants to watch Psycho. Cassidi, onthe other hand, prefers to watch more recent horror movies and would like to seeMidsommar. Each girl gets a payoff of 10 if they watch her preferred movie and gets payoff of 5 if they watch the movie her sister chose. Since Cassidi suggested the movie they watched last time, it's Brooke's turn to begin with the movie suggestion. So Dan first asks Brooke for her preference, then asks Cassidi her choice after she hears Brooke's suggestion. Each girl can choose eitherPsycho (P) or Midsommar (M). If both girls choose the same movie, then that's themovie that they are going to watch. If the girls disagree on the movie, then Dan stepsin and makes the final decision. Dan has an additional movie that he can choose, whichis secretly his favorite: Frozen (F). This is Brooke and Cassidi's least favorite optionand they each get a payoff of 1 if they end up watching Frozen.Dan is happiest if they watch a movie without girls disagreeing and fighting, so hispayoff is 8 whether they watch Psycho or Midsommar as long as the girls agree on themovie. He gets a payoff of 2 if he favors one of her daughters over the other and picksPsycho or Midsommar even though the girls couldn't agree which one to watch. Hegets a payoff of 7 if he gets to make a choice and they end up watching Frozen.

a. Draw this game in extensive form. Make sure you include payoffs forall players (write the first payoff for Brooke, second one for Cassidi, and third onefor Dan in each terminal node).

b. What is the Subgame Perfect Nash Equilibrium of this game? Use back-wards induction. (Show your work on the decision tree by highlighting relevant branches while doing backwards induction).

c. How many possible strategies does Brooke have? Write down each one.

d. How many possible strategies does Cassidi have? Write down each one.