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Take Home Midterm Exam (2014)
Posted Date: March 9, 2014 (Bring your answer sheets in class on March 11) Subject: Game Theory (ECO290E)
Instructor: Yosuke YASUDA
1. Dominant Strategy (7 points)
a) Explain the difference between “dominant strategy” and “dominated strategy”. b) Construct a static game in which, 1) there are two players, 2) each player has at
least three strategies, and 3) a unique outcome is derived by the iterated elimination of dominated strategies.
Remark: You can just draw a payoff matrix that satisfies 1) through 3).
2. Simple 2‐2 Games (9 points)
For each static game A, B, and C below, answer the following questions: i. Explain whether there exists a dominant strategy.
ii. Find (all) pure‐strategy Nash equilibrium if it exists. iii. Find (all) mixed‐strategy Nash equilibrium if it exists.
A)
P1＼P2 C D
A 2, 3 0, 5
B 3, 2 1, 1
B)
P1＼P2 G H
E 3, 3 1, 4
F 4, 1 0, 0
C)
P1＼P2 K L
I 2, ‐2 ‐1, 1
J ‐1, 1 3, ‐3
2
3. Game with Continuous Strategies (7 points)
Consider a location game (Hoteling model) analyzed in class, but with different preferences for the players. Instead of each player seeking to sell as many ice‐creams as possible, suppose that each wants to sell as few ice‐creams as possible.
a) Derive all pure strategy Nash equilibria of this game.
b) Provide a realistic story that would reasonably fit this modified location game.
4. Dynamic Game (9 points)
Consider a dynamic game depicted by Figure 1. a) How many strategies does each player have?
b) Express this game into normal‐form by drawing a payoff matrix, and then find all Nash equilibria.
c) Solve the game by backward induction and show that which Nash equilibrium in (b) survives.
5. Focal Point (3 points)
Select a country, and write down its name. You can choose any country in the world, but should not write more than one name. If you will successfully choose the most popular answer, you would get 3 points. Otherwise, you will receive 0. You do not need to explain any reason why you choose your answer.
1
2
2
A
B
C
D E
F
(1, 1)
(4, 2)
(3, 1)
(2, 5)
Figure 1
