212.339 Game theory and Applications 2009 Autumn
In Ho Lee
Problem Set 1
(Due date : Sep, 22)
1. Suppose that the information partitions of two agents, A and B, are given as
follows:
P A 1, 2, 3, 4, 5, 6
P B 1, 2, 3, 4, 5, 6
Suppose that 3, that is, 3 is
212.339 Game theory and Applications 2009 Autumn
In Ho Lee
Problem Set 3
(Due date : Oct, 20)
1. Suppose that two players play each other for two periods. In the rst period they play
the rst game below, and in the second period they play the second game b
4. Assume there is a pure strategy NE, (e , e ). If e > e , then player 1 (P1) (strictly) prefers
12
1
2
e
1
to e because from such deviation P1 get the same grade A, but pays less disutility. In
1
the same logic, if e < e , then player 2 (P2) (strictly)
212.430 Game Theory and Applications 2001
In Ho Lee
Mid-Term Examination
October 24, 2001
1. Is the following game dominance solvable? Identify the Nash equilibrium in pure strategies.
U
D
L
4, 3
5, 5
M
2, 7
5, -1
R
0, 4
-4, -2
2. There are k witnesses to
212.339 Game theory and Applications 2008 Autumn
In Ho Lee
Problem Set 4
(Due date : October 18th)
1. We have two partners who simultaneously invest in a project, where the level of
investment can be any non-negative real number. If partner i invests x i
212.339 Game theory and Applications 2008 Fall
In Ho Lee
Problem Set 1
(Due date : Sep, 25)
1. Consider two players play Rock, Scissors, and Paper. Rock wins Scissors, Scissors
wins Paper, and Paper wins Rock. If both players choose the same action, they
212.339 Game Theory and Applications 2006
In Ho Lee
Problem Set 3
(due Nov. 21)
1. Consider a game in which the following simultaneous move game is played twice. There is
no discounting unless stated otherwise.
b1
b2
b3
a1
8,8
3,10
0,12
a2
10,3
7,7
0,0
a3
212.339 Game Theory and Applications 2006
In Ho Lee
Problem Set 1
(due Oct. 3)
1. Consider two players play Rock, Scissors, and Paper. Rock wins Scissors, Scissors
wins Paper, and Paper wins Rock. If both players choose the same action, they draw. The
win
212.339 Game Theory and Applications 2004
In Ho Lee
Final Examination
December 6, 2004
1. Consider two rms play duopoly with the supply quantity as their strategy. The market demand
is given by p = a Q where p is the price and Q = q1 + q2 is the total sup
212.339 Game theory and Applications 2003
In Ho Lee
Final Examination
December 8, 2003
1. Consider the following adaptation of Akerlofs lemons model. Used cars are of three
possible quality levels cfw_L, M, H . Let the buyers valuations be b(L) = 14, b(M
212.339 Game theory and Applications 2014 Autumn
In Ho Lee
Final Exam
(2014, December 9)
1. (50 points) Consider Hotellings beach where two ice cream shops are located at two ends
of a beach with distance 1. Consumers are continuously distributed uniforml
212.339 Game theory and Appications 2003
In Ho Lee
Mid-Term Examination
October 20, 2003
1. (10 points) Carefully dene Nash equilibrium and subgame perfect equilibrium.
2. (10 points) What is the meaning of rationality in game theory? Explain its role in
212.339 Game theory and Applications 2004
In Ho Lee
Mid-Term Examination
October 25, 2003
1. A group of n students go to a restaurant. It is common knowledge that each student will
simultaneously choose his own meal, but all students will share the total
212.339 Game theory and Applications 2009 Autumn
In Ho Lee
Problem Set 4
(Due date : Nov, 17)
1. Suppose the agent utility is V = u(w) -c(e), where we assume that the agent outside
s
s
opportunity u = 0:The principal0 s payo is = x - w where w is paid for
212.339 Game theory and Applications 2009 Autumn
In Ho Lee
Problem Set 2
(Due date : Oct, 6)
1. Find the set of Nash equilibria of each player in the two-player game in the
following figure.
a1
a2
a3
a4
b1
b2
0, 7 2, 5
5, 2 3, 3
7, 0 2, 5
0, 0 0, 2
b3
b4
212.339 Game theory and Applications 2008 Autumn
In Ho Lee
Midterm Exam
(October 28, 2008)
1. Two drivers, player 1 and player 2, are simultaneously approaching an intersection
from different directions. They may choose to stop (S) or continue (C) at the
212.339 Game theory and Applications 2008 Autumn
In Ho Lee
Problem Set 5
(Due date : December 4)
1. Consider the following adaptation of Akerlofs lemons model. Used cars are of three
possible quality levels L, M, H. Let the buyers valuations be bL 14,
bM
212.339 Game theory and Applications 2008 Autumn
In Ho Lee
Problem Set 3
(Due date : Oct, 21st)
1. Answer the following questions.
Pic. a
Pic. b
(a) Find the SPE of the game for "Pic. (a)" by backward induction.
(b) Find all Nash and all subgame perfect N
212.339 Game theory and Applications 2008 Autumn
In Ho Lee
Problem Set 2
(Due date : Oct, 7)
1. Find the set of Nash equilibria of each player in the two-player game in the
following figure.
a1
a2
a3
a4
b1
b2
0, 7 2, 5
5, 2 3, 3
7, 0 2, 5
0, 0 0, 2
b3
b4
212.339 Game theory and Applications 2008 Autumn
In Ho Lee
Final Exam
(December 9, 2008)
1. Two firms compete in a market. Let q 1 and q 2 be the production quantities of firm 1
and firm 2 respectively. Assume that firm 1 can only choose q 1 10 or q 1 5,
212.339 Game Theory and Applications 2007
In Ho Lee
Final Examination
December 6, 2007
1. The market demand for a good is given by the following inverse demand function: P (Q) =
Q; whereby Q denotes the overall supplied quantity, and P(Q) denotes the mar-
212.339 Game theory and Applications 2007
In Ho Lee
Midterm Examination
October,30 2007
1. Consider the following game :
a1
a2
b1
b2
10; 5 3; 6
x; 6 0; 0
Here x can be any real number.
(a) For what values of x is the game dominance solvable?
(b) For what
212.339 Game Theory and Applications 2006
In Ho Lee
Problem Set 4
(due 5. Dec)
1. Consider the following Cournot duopoly. The inverse demand function is given by
P = a Q . Firm 1 has a known constant marginal cost and firm 2 has uncertain marginal cost
wh
212.339 Game Theory and Applications 2006
In Ho Lee
Problem Set 2
(due Oct. 10)
1. A group of n students go to a restaurant. It is common knowledge that each student will
simultaneously choose his own meal, but all students will share the total bill equal
212.339 Game theory and Applications 2005
In Ho Lee
Mid-Term Examination
October 26, 2005
1.
(a) Carefully dene common knowledge.
(b) Explain the critique of subgame perfect equilibrium using the centipede game.
(c) Suppose that the rationality of the pla
212.339 Game theory and Applications 2009 Autumn
In Ho Lee
Problem Set 5
(Due date : Dec, 1)
1. Consider the following strategic situation. Two opposed armies are poised to seize an
island. Each army general can choose either "attack" or "not attack". In