Question

The political figures Rosa and Ernesto have to choose either Berlin (B) or Havana (H) as the location for a party congress. They choose sequentially. A third person, Karl, determines who chooses first. Both Rosa and Ernesto care only about the actions they choose, not about who chooses first. Rosa prefers the outcome in which both she and Ernesto choose B to that in which they both choose H, and prefers this outcome to either of the ones in which she and Ernesto choose different actions; she is indifferent between these last two outcomes. Ernesto’s preferences differ from Rosa’s in that the roles of B and H are reversed. Karl’s preferences are the same as Ernesto’s.

a. Draw this game's extensive form

b. Identify all the pure strategies for the 3 players of this game

c. Find the rollback equilibrium for this game