Answers to HW 1
1. Sample space is composed of 52 elements such as
cfw_A,2,3,4,5,6,7,8,9,10,J,Q,K associated with 4 different suits. For
instance, the probability of event cfw_A,J is assigned as p(A,J) =
8/52=2/13
2. 1/3; 2/3; b-a, if b a .
1
3. p(L|U)=0,
Sp'04
Prof. Stahl
Eco 354K
Midterm Exam #1
(5%) Put only your Student ID on your answer sheets, and start each answer on a
new page.
1. (20%)
a)
b)
c)
d)
Briefly define the following terms:
event;
information set;
perfect recall;
perfect information.
2. (
Solutions to
Problem Set No. 5
1. Represent the game of Marienbad with a starting configuration of 3 matches
in each pile in extensive form.
Marienbad: There are two piles of matches and two players. The game starts
with player 1 and thereafter the player
Prof. Stahl
354K Game Theory
Problem Set No. 4b
1) Tadelis, 2.3 (a) and (b).
2) Tadelis, 2.7 (a).
3) Tadelis, 2.10 (a) (f). CAUTION: There is a typo in the first sentence;
will die in 6 months should read will die in 3 months.
Econ 354K
Game Theory
Solutions to Problem Set No. 11b
1. Infinitely Repeated Chicken
(a) Subgame perfect NE:
Grim strategy: Play C in period 1 and in any period which has a history of
everyone playing C. However, in any period in which someone has played
Econ 354K
Game Theory
Solutions to Problem Set No. 11a
1. Loan
(a) Its because you do not have $500 for the full year. You make monthly
payments.
13
1
n
12
1 n 1 0 1 n
1
1+ r
1
1
55
= 55
= 55
1
1
n =1 1 + r
n = 0 1 + r 1 + r n =13 1 + r
1
1
Prof. Stahl
354K Game Theory
Problem Set No. 4
Due Feb 10
1) Ronald is indifferent between $50 for sure and a 25% chance of $500 or
nothing. He is also indifferent between $25 for sure and a 15% chance of $500
or nothing. (a) Assuming Ronald's preferences
Econ 354K
Game Theory
Solutions to
Problem Set No. 7
1. Dutta 3.8: Art Auction - Strategies
Strategies available for both bidders:
2,000; 3,000; 4,000; 5,000; 6,000; 7,000; 8,000; 9,000.
2. Dutta 3.9: Art Auction Strategic Form
We restrict attention to st
S'11
Prof. Stahl
354K Game Theory
Problem Set No. 3;
Due: Thursday, Feb 3
1) An executive at a publishing house has just received two stock options as a bonus.
Each of these options gives the executive the right (but not the obligation) to purchase
one sh
Econ 354K
Game Theory
Solutions to Problem Set No. 11a
1. Loan
(a) Its because you do not have $1000 for the full year. You make monthly
payments.
12
100 (
n =1
1n
1n
10
1n
) (
) (
) ] = 100[
) = 100[ (
1+ r
1+ r
n =0 1 + r
n =13 1 + r
(b)
1
1
1
1+ r
1 (
S '11
Prof. Stahl
Eco 354K - Problem Set 5
Due: Feb 24
1. Dutta, 11.4
2. Dutta, 11.5
3. (a) Solve the following game by backward induction. [There are two such solutions.]
1.1
L
M
2.1
2.2
u
3.2
l' c'
02
03
03
r'
1
0
2
R
d
u' m'
1.2
L' M' R'
1
4
2
3.1
2
0
Econ 354K
Game Theory
Solutions to
Problem Set No. 2
1. Draw the firms decision tree.
Manila
ship
2
truck
4
New York
train
3
New York
($100)
ship
truck
($111)
train
ship
($125)
train
New Orleans
ship
truck
truck
($112)
New Orleans
5
train
New Orleans
($95
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Prof. Stahl
354K Game Theory
Problem Set No. 2
Due: Thursday, Jan 27
1) The Electa Company has to ship 10,000 television sets from its factory in Manila to an
American importer in New York City. As can be seen in Figure 1, the firm can either ship th
S'11
Prof. Stahl
ECO 354K
Problem Set No. 10
Due Friday, April 8 by 5pm
Note: Please submit your completed HW to the Econ front desk for the TA.
Write Jonathan Lhost at the top and have them time stamp it.
1. Consider the following game with payoff uncert
S11
Prof. Stahl
354K Problem Set No. 11a
Due April 21
1. Your local loan agency lends you $1000, and you must make 12 monthly
payments of $100 each (totaling $1200), with the first payment in one month.
(a)
Why is your annual interest rate not equal to $2
ECO 354K
Problem Set No. 7
Due Thursday, March 10
1) Dutta: 3.8
2) Dutta: 3.9
3) Dutta 3.22 (Modified as follows). Assume that player 1 wins the drawing when
both players choose identical maximum bids, and identify the strategies that are
not weakly domin
Eco 354K
Game Theory
Solutions to
Problem Set No. 4
1. Ronalds preference
(a) The ranking is B > C > A.
U($50)=.25U($500), U($25)=.15U($500). So let U($500)=1, U($0)=0,
Then U($50)=.25 and U($25)=.15.
U(PA)=.05U($500)+.3U($50)+.3U($25)+.35U($0)=.17
U(PB)=
ECO 354K
Problem Set No. 8
Due: March 24
1.
Dutta: 5.2.
2.
Dutta: 5.4.
3.
Dutta: 5.5.
4. There are three television stations in a city, each affiliated with one of
the three major networks: ABC, CBS and NBC. All three stations have the
option of running t
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Prof. Stahl
ECO354K, Unique No. 34495
INTRODUCTORY GAME THEORY SYLLABUS
TTH 2-3:30, BRB 1.118
Content:
This course will introduce upper-level undergraduates to game theory,
which has made recent significant contributions in every field of economics
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Prof. Stahl
Eco 354K - Problem Set 6
Due: March 3
1. The Military Draft. During the Vietnam War, the US government wanted to motivate
teenagers to register for the military draft. The problem faced by the government was that it
would be impossible t
Answers to HW 4b
1. Tadelis 2.3
(a)
1.1
Lassie
Snoopy
None
N
N
(0.7) W
$0
L
$1
W
$10
-$1
Expected payoff given Lassie = $0.4.
Expected payoff given Snoopy = $0.1.
(b)
(0.9) L
-$1
Therefore, Lassie is best bet.
Let "AI" denote anti-insurance.
1.1
Lassie
Sn
Eco 354K
Solutions to PS 10
1.
L
U -2, 0
D 0, 5
B
L
R
U 0, 0 5, -2
D -2, 7 7, 5
A
a) No information; prob(A) = 2/3
R
5,-2
7, 7
L
R
U -2/3, 0
5, -2
D -4/3, 19/3 7, 17/3
NE = (U,L)
b) Only player 1 observes outcome of die throw.
N
B
A
1.2
1.1
D
U
D
U
2.1
L
S'07
Prof. Stahl
354K - GAME THEORY
Exam 2
* (5%) Do NOT put your name on any answer pages.
Put your 4-digit ID number ONLY at the top of every answer page.
Start your answer for each question on a new page.
1. (20%)
Definitions:
(a) Give a precise defini
Econ 354K
Game Theory
Solutions to Problem Set No. 11b
1. Game of Chicken
Minimax: max U1(,C)=1+x; max U1(,S)=0 => min(1+x,0)=0. Therefore minimax is
(0,0).
IR set: area (0,1+x)-(0,0)-(1+x,0)-(1,1)
U2
(0, 1+x)
(1, 1)
U1
(1+x, 0)
(-1, -1)
minimax (0, 0)
2
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Prof. Stahl
354K
Game Theory
Problem Set No. 1
Due: Tuesday, Jan 25
1) Consider the uncertainty associated with drawing a card from a deck of cards.
List the sample and event spaces (you do not have to list all possibilities but
list the categories).
Prof. Stahl
354K - GAME THEORY
Sample Exam
* (2.5%) Put your 4-digit code ONLY at the top of every answer sheet.
* (2.5%) Start your answers for each question at the top of a NEW page.
1. (40%) Bubba Wildcat has the opportunity to buy a tract of land unde
SAMPLE EXAM 2
354K - GAME THEORY
*
Prof. Stahl
(5%) Do NOT put your name on any answer page.
Put your 4-digit ID number ONLY at the top of every answer page.
Start your answer for each question on a new page (or back side).
1. (20%) Two clothing stores in
ECO 354K
Solutions to HW7
1.
A
C
D
W
2, 3
-1, 2
0, 4
4, 0
X
3, 3
3, 2
-1, 1
2, 1
Y
First B strictly dominates D, so eliminate D.
Second, Y iteratively strictly dominates W, so
eliminate W. Third, B iteratively strictly
dominate C, so eliminate C. What rem