1
Take Home Midterm Exam
Date: March 11, 2009 (Return your answer sheets to my mail‐box by 12:00 on 13th) Subject: Game Theory (ECO290E)
Instructor: Yosuke YASUDA
1. Dominant Strategy
Explain the difference between “dominant strategy” and “dominated strategy”.
2. Simple 3‐3 Game
Consider the following 3‐3 game.
P1 / P2 D E F
A 7, 6 5, 8 0, 0
B 5, 8 7, 6 1, 1
C 0, 0 1, 1 4, 4
a) Is there any dominant strategy in this game? Explain why. b) Find the pure strategy Nash equilibria.
c) Find the mixed strategy Nash equilibrium in which each player randomizes over just the first two actions, i.e., A, B and D, E respectively.
d) Compute players’ expected payoffs in the equilibria found in parts (b) and (c).
3. Game with Continuous Strategies
Two neighboring homeowners, i=1, 2, simultaneously choose how many hours li to spend maintaining a beautiful lawn. The average benefit per hour is:
10 – li + lj/2
Assume the (opportunity) cost per hour for each is 4. Homeowner i’s average benefit is increasing in the hours neighbor j spends on his own lawn, since the appearance of one’s property depends in part on the beauty of the surrounding neighborhood.
a) Compute the Nash equilibrium.
b) Graph the best‐response functions and indicate the Nash equilibrium on the graph. c) Solve the Nash equilibrium when the cost of one owner changes from 4 to 2, but
the other’s remains the same. Give an economic intuition to your result.