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. Model this situation as an extensive game with perfect information.

b. Using backwards induction. What is your prediction about this situation? Where will the congress be held?

Answer 1

Lets first understand the components of extensive game with perfect information : ( You may also refer An introduction of game theory book by Martin)

(Extensive game with perfect information) An extensive game with perfect information consists of :

• a set of players

• a set of sequences (terminal histories) with the property that no sequence is a proper subhistory of any other sequence

• a function (the player function) that assigns a player to every sequence that is a proper subhistory of some terminal history

• for each player, preferences over the set of terminal histories.

The set of terminal histories is the set of all sequences of actions that may occur; the player assigned by the player function to any history h is the player who takes an action after h.