Chapter 9 Textbook Problems
Chapter 9: Bayesian Games
282.1 (Fighting an Opponent of Unknown Strength) *Very Likely!*
Two people are involved in a dispute. Person 1 does not known whether person 2 is strong or weak; she
assigns probability to person 2s be
Chapter 10 Textbook Problems
Chapter 10: Extensive Games with Imperfect Information
319.3 (Nash Equilibria of Card Game)
Each of two players begins by putting a dollar in the pot. Player 1 is then dealt a card that is equally likely
to be High or Low; she
ECON 4020 - Game Theory
Solutions: Homework 0
test your knowledge of probability theory
Due date and time: September 4, 2013 - in class
1. Consider two sets, A = cfw_1, 2 and B = cfw_x, y, z. Write down the Cartesian product of these two sets:
A B.
A B =
2. If a player has a dominant strategy in a simultaneous-move game, then she is sure to get her
best outcome. True or false? Explain and give an example of a game that illustrates your
answer.
4. Suppose the market demand is described by D(p) = a p for p
ECON 4020 - Game Theory
Homework 7
Due date and time: December 6, 2013 - in class
1. Consider the following version of the entry game:
Challenger
Out
Ready
U nready
Incumbent
2, 4
A
F
3, 2
1, 1
A
F
4, 2
0, 3
(a) Model this situation as an extensive game w
ECON 4020 - Game Theory
Homework 6
Due date and time: November 27, 2013 - in class
1. There are two individuals, each can be either type A or B. There is a task that has to be completed,
only one apt person is required to complete it. Type A is capable of
ECON 4020 - Game Theory
Homework 4
Due date and time: November 1, 2013 - in class
1. Two rms, rm 1 and rm 2, must decide whether to enter a new industry. Industry demand is
P = 900 Q. To enter the industry a rm must build a production facility of one of t
ECON 4020 - Game Theory
Homework 5
Due date and time: this HW is optional, it will not be graded; solutions will be posted on
November 6
1. Consider the following game with two states, A and B. Each state is equally likely. Payos are:
U
M
D
L
6, 0
0, 0
5,
ECON 4020 - Game Theory
Homework 2
Due date and time: October 2, 2013 - in class
1. Consider a two-player, two-strategy game where the payos are independent random draws from a
uniform distribution on [0, 1]. What is the probability that (U, L) is a NE?
U
Cournot model with xed costs
Game: 2 rms, compete by choosing quantities they produce/sell. The product is homogeneous, and
the choices are made simultaneously. The demand for the product is given by inverse demand function
P (Q) = A BQ, where Q is the ag
The war of attrition
Game: 2 animals ght over an indivisible prey (two rms compete for the right to stay in the market
which is too small for two). The prey is worth vi to each i cfw_1, 2. Each animal decides the time at which
it will stop ghting, ti . Th
Spring 2015
Econ 4020
Problem Set 0
The purpose of this problem set is to provide you with examples of the kinds
of probability calculations we will be doing in the second half of the course.
The problems labelled with a are the baseline you should know h
Hembrooke and Gay
Journal of Computing in Higher Education
Fall 2003, Vol. 15(1), ?-?.
The Laptop and the Lecture:
The Effects of Multitasking in
Learning Environments
Helene Hembrooke and Geri Gay
Human Computer Interaction Laboratory
Cornell University
Econ 4020
Game Theory
Nash Equilibrium I
1. Two players are playing the following card game. Each player has a deck of cards. The
rst player puts down a card. Seeing this, the second player puts down a card. Payos
are as follows: If either card is an hono
Spring 2015
Econ 4020
Problem Set 0
The purpose of this problem set is to provide you with examples of the kinds
of probability calculations we will be doing in the second half of the course.
The problems labelled with a are the baseline you should know h
Econ 4020
Game Theory
Nash Equilibrium & Subgame Perfection
1. In the game below, player 1 chooses rows, 2 chooses columns and three chooses matrices.
Only player 3s payos are indicated. Show that action D is not a best response to any
mixed strategy prol
524581
research-article2014
PSSXXX10.1177/0956797614524581Mueller, OppenheimerLonghand and Laptop Note Taking
Psychological Science OnlineFirst, published on April 23, 2014 as doi:10.1177/0956797614524581
Research Article
The Pen Is Mightier Than the Keyb
ECON 4020 - Game Theory
Homework 0
test your knowledge of probability theory
Due date and time: September 4, 2013 - in class
1. Consider two sets, A = cfw_1, 2 and B = cfw_x, y, z. Write down the Cartesian product of these two sets:
A B.
2. Lottery ticket
ECON 4020 - Game Theory
Department of Economics, Cornell University
Fall, 2013
Instructor: Olena Rarytska
oce hours: 2 pm - 3 pm, Mondays, Wednesdays, or by appointment
oce: Uris Hall, 444
e-mail: or57
Organization: lecture time is 11:15 am - 12:05 pm, Mo
Econ 4020 Game Theory
6. Extensive games with
imperfect information
Extensive games
Extensive games
with perfect information players are informed
about actions chosen by other players at the
previous moves
with imperfect information a player when
choosi
ECON 4020 - Game Theory
Solutions: Homework 1
Due date and time: September 20, 2013 - in class
1. Consider the following game
X
Y
Z
A
1,1
2*,5
1,3
B
0,0
0,1
2*,1
C
-2,4*
1,0
2*,4*
D
1*,-1
1*,6*
0,4*
(a) Find strictly dominated strategies if there any
B is
ECON 4020 - Game Theory
Homework 2
Due date and time: October 2, 2013 - in class
1. Consider a two-player, two-strategy game where the payos are independent random draws from a
uniform distribution on [0, 1]. What is the probability that (U, L) is a NE?
U
ECON 4020 - Game Theory
Homework 3
Due date and time: October 21, 2013 - in class
1. (Based on exercise 130.3) Pairs of players from a single population bargain over division of a pie of size
10. The members of a pair simultaneously make demands; the poss
ECON 4020 - Game Theory
Homework 5
Due date and time: this HW is optional, it will not be graded; solutions will be posted on
November 6
1. Consider the following game with two states, A and B. Each state is equally likely. Payos are:
U
M
D
L
6, 0
0, 0
5,
ECON 4020 - Game Theory
Solutions: Homework 6
Due date and time: November 27, 2013 - in class
1. There are two individuals, each can be either type A or B. There is a task that has to be completed,
only one apt person is required to complete it. Type A is
ECON 4020 - Game Theory
Solutions: Homework 4
Due date and time: November 1, 2013 - in class
1. Two rms, rm 1 and rm 2, must decide whether to enter a new industry. Industry demand is
P = 900 Q. To enter the industry a rm must build a production facility
ECON 4020 - Game Theory
Solutions: Homework 7
Due date and time: December 6, 2013 - in class
1. Consider the following version of the entry game:
Challenger
Out
Ready
U nready
Incumbent
2, 4
A
F
3, 2
1, 1
A
4, 2
F
0, 3
(a) Model this situation as an exten
Name (print): _
ID: _
ECON 4020 Game Theory
Prelim Exam I
Note: The exam is closed book, closed notes. No programmable calculators are
allowed, and phones or internet devices cannot be used during the exam.
Please, show your work. Good luck!
1. Consider t
ECON 4020 Game Theory
Prelim Exam II (Make-Up)
Note: The exam is closed book, closed notes. No programmable calculators are
allowed, and phones or internet devices cannot be used during the exam.
Please, show your work. Good luck!
2. Consider the followin