Economics (Game Theory)
All extra credit points are added to your total score at the end of the semester.
Problem 1: Answer only if your midterm score is below 60% (10 points)
C
D
N
C
3, 3
4, -1
-2, -2
D
-1, 4
0, 0
-2, -2
N
-2,-2
-2, -2
-2, -2
a. Are there any pure strategies of any player that are strictly dominated?
b. Are there any pure strategies of any player that are weakly dominated?
c. Find all pure strategy Nash equilibria of the game.
Problem 2: Answer only if your midterm score is below 70% (10 points)
The following game theoretic model illustrates the strategic aspects of tariffs (taxes
on imports).
Suppose two countries are fighting a tariff war. Let xi ∈ [0, 100] be the level of tariff
(a percentage number) picked by country i = 1, 2. If country i selects xi and the other
country selects xj , then country i gets a payoff of 2000 + 60xi + xi xj − x2i − 90xj . (Each
country chooses a tariff level independently and simultaneously.)
a. Find the best response functions for the countries.
b. Find the Nash equilibrium of the game.
Problem 3: Open to all (10 points)
a. Find all NE (pure as well as mixed strategy) of the first game.
b. In the second game, show that the countries would be better off if they jointly
agreed to set lower tariffs.