(Strategies in extensive games) What are the strategies of the players in the entry game (Example 153.2)? What are Rosa’s strategies in the game?

Example 153.2

Examples of extensive games with perfect information)

a. Represent in a diagram like Figure 154.1 the two-player extensive game with perfect information in which the terminal histories are (C, E), (C, F), (D, G), and (D, H), the player function is given by P(∅) = 1 and P(C) = P(D) = 2, player 1 prefers (C, F) to (D, G) to (C, E) to (D, H), and player 2 prefers (D, G) to (C, F) to (D, H) to (C, E).

b. Write down the set of players, set of terminal histories, player function, and players’ preferences for the game in Figure 158.1.

c. The political figures Rosa and Ernesto each has to take a position on an issue. The options are Berlin (B) or Havana (H). 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. Model this situation as an extensive game with perfect information. (Specify the components of the game and represent the game in a diagram.)