2. (2 points) Arjun and Bianca are visiting Cho's apartment to watch and the three of them are choosing which movie to watch.

Arjun would prefer to watch the 2006 monster movie The Host (H), while Bianca has been wanting to see the gritty postapocalyptic Snowpiercer (S). Each of them gets a payoff of 5 is they watch their preferred movie and a payoff of 3 if the group ends up watching the other of these two films. Cho has seen and likes both movies, so her payoff would be a 4 if the group watched either of these two.

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EC 327, Spring 2021 Problem Set 2 University of Oregon

Cho, the hostess, asks Arjun for his preference between The Host (H) and Snowpiercer (S), and then she asks Bianca which she would like to watch after they both hear Arjun's reply. If Arjun and Bianca each choose the same movie title the three of them will watch that movie. If Arjun and Bianca choose different movies, Cho will make the tiebreaking decision. As the hostess, in addition to The Host and Snowpiercer Cho also has a third option: put on the zombie thriller Train to Busan (T), which would give Cho a payoff of 5 but leave Arjun and Bianca each a payoff of 2, since those two are less excited about zombies.

1. a)Draw the tree for this game. Label the players' decision nodes as well as the actions, and write the payoffs at the terminal nodes.
2. b)How many complete strategies does Bianca have in this game? Briefly explain your answer.
3. c)How many complete strategies does Cho have in this game? Briefly explain your answer.
4. d)What are the players' rollback equilibrium strategies in this game? What are the payoffs in equilibrium?