Posted: November 25th, 2015

Economics (Game Theory)

Economics (Game Theory)

Represent as a game tree, 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(Ø)=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).
Problem 2 (Advanced)
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. 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. Use the game tree format.
Problem 3 (Basic-Advanced)
a. What are the strategies of the players in the following entry game?
b. What are Rosa’s strategies in Problem 2?
Challenger
In Out
Incumbent
Acquiesce Fight
2, 1 0, 0
1, 2
Problem 4 (Basic)
a. Find the Nash equilibria for the game described in Problem 1.
b. Find the Nash equilibria for the following game.
Problem 5 (Advanced)
For the following game:
a. Write the normal form representation.
b. Find all pure strategy Nash equilibria.
c. Determine which of these Nash equilibria is subgame-perfect.
1
C D
2
E F
3, 1
2, 0
G H
1
1, 2 0, 0
2
1
Y Z
2
L R
X
2, 2
L R
3, 1 0, 0 5, 0 0, 1

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