ECN 122 Game Theory: Homework 3
Deadline: Friday, October 23, 2015, 3:10 pm at the beginning of the
class
Practice Problems
Exercise 38.2 (Dividing money) Two people have $10 to divide between themselves.
They use the following procedure. Each person name
University of California, Davis - Department of Economics
ECON 122 : GAME THEORY
Professor Giacomo Bonanno
PRACTICE FOR FIRST MIDTERM EXAM
Answer all questions. Explain your answers.
1. Two players can make a total profit of $100 if they are not too greed
ECN 122 Game Theory: Homework 8
Deadline: Tuesday, December 8, 2015, 3:30 pm at the beginning of the
nal exam
Practice Problems
Exercise 163.31 (Nash equilibria of extensive games) Find the Nash equilibria
of the games in Exercise 156.2a and Figure 160.1.
ECN 122 Game Theory: Homework 1
Deadline for graded problems: Friday, October 9, 2015, 3:10 pm in class
Practice Problems
Exercise 5.3 (Altruistic preference) Person 1 cares about both her income and person
2s income. Precisely, the value she attaches to
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 3 ANSWERS
1. (a)
Note: N = not file, F = file, a = audit, n = not audit.
(b) The normal form is as follows (the numbers are expected payoffs):
TA-2
N
F
N 625,625, 250C
TA-1
TA-2
1
625,700,17
ECN 122 : Game Theory
Professor Giacomo Bonanno
WINTER 2017 - SECOND MIDTERM EXAM: ANSWERS for VERSION 2
1. (a) For example, ACG.
(b) Four. (c) First solve the subgame on the left:
Player 2
E
F
C
2
4
3
3
D
1
6
9
5
Player 1
There is a unique Nash equilibri
ECN 122 : Game Theory
Professor Giacomo Bonanno
Winter 2017 - FIRST MIDTERM EXAM: ANSWERS for VERSION 2
Note: this exam was based on the material covered in class on January 20, 2017 and in the
textbook pp. 22-24.
(a) (2,33) 1 (2,58) 1 (1,70) .
(b) (1,75)
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 3 ANSWERS
(a) The extensive game is as follows (W means withdraw and N means Not withdraw)
1
W
N
2
W
80
80
N
W
100
60
60
100
N
1
N
W
2
W
N
150
150
200
100
W
N
100
200
150
150
(b) Only one pr
Professor Giacomo Bonanno
ECONOMICS 122 GAME THEORY
~
HOMEWORK # 4 ANSWERS
First we solve the subgame on the right. The strategic form is
Player 2
M
N
H
4
0
0
3
L
0
1
1
0
Player 1
There is no pure-strategy Nash equilibrium. To find the mixed-strategy Nash
ECN 122 : Game Theory
Professor Giacomo Bonanno
Winter 2017 - FIRST MIDTERM EXAM: ANSWERS for VERSION 1
Note: this exam was based on the material covered in class on January 20, 2017 and in the
textbook pp. 22-24.
(a) (1,72) 1 (2,35) 1 (2,60) .
(b) (2,46)
ECN 122 : Game Theory
Professor Giacomo Bonanno
WINTER 2017 - SECOND MIDTERM EXAM: ANSWERS for VERSION 1
1.
(a) Neither Player 1 nor Player 3 have a strictly dominated strategy. For Player 2 C is
strictly dominated by D.
(b) At a Nash equilibrium no stric
ECN 122 Game Theory: Homework 6
Deadline: Friday, November 13, 2015, 3:10 pm at the beginning of class
Practice Problems
Exercise 87.1 (First-price Sealed-bid Auction) Show that in a Nash equilibrium
of a rst-price sealed-bid auction the two highest bids
ECN 122 Game Theory: Homework 5
Deadline: Friday, November 6, 2015, 3:10 pm, at the beginning of class
Practice Problems
Exercise 63.1 (Interaction among resource users) A group of n rms uses a common resource (a river or a forest, for example) to produce
ECON 122 : GAME THEORY
Professor Giacomo Bonanno
PRACTICE FIRST MIDTERM: ANSWERS
1.
(a) 10 is not strictly dominated for Player 1 (if Player 2 writes 90, then writing 10 gives Player 1
a payoff of $10, while every other strategy gives him $0).
(b) Player
than dxﬂuﬂiﬁ «ash
Mn they 9
'CQL ﬁmmg.
Q
lbw-ma. " 0.2 {73 4'14 mm cm”! !£ 1 [:51 I W m
me wet-web-
: “Q‘Qc‘i'léﬁ-i " ‘14.; . _._._
= “*M ‘ {a ' c. H9 f WWW" “W
' Ju'lgadvd
Q“: ﬂ
Professor Giacomo Bonanno
ECONOMICS 122 GAME THEORY
~
HOMEWORK # 1 ANSWERS
1. (a) The game is as follows:
Player 1
A
B
C
6
8
9
D
3
0
3
0
0
2
3
4
0
Player 2
E
1
4
1
2
0
1
0
1
5
F
0
2
0
4
4
0
6
7
2
F
2
0
0
6
5
1
Player 3: G
Player 1
A
B
C
0
4
9
D
0
5
0
1
1
Professor Giacomo Bonanno
ECONOMICS 122 GAME THEORY
~
HOMEWORK # 6 ANSWERS
1. (a) The strategic form is as follows:
Player 2
l
Player 2
r
l
r
R
1 , 0 , 0
1 , 0 , 0
R
1 , 0 , 0
1 , 0 , 0
Player
M
0 , 1 , 1
2 , 2 , 1
M
0 , 1 , 0
0 , 0 , 0
1
L
0 , 1 , 0
0 ,
Chapter 1
The Theory of Rational
Choice
The Theory of Rational Choice
A rational decision-maker chooses the best
action according to her preferences, among
the actions available to her.
Set of available actions
Preferences
Complete
Consistent (transitive)
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
ANSWERS TO PRACTICE PROBLEMS for WEEK 10
1.
(a) In Harsanyis theory a strategy for a player specifies an action for each one of
his types. Albert has tw
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
ANSWERS TO PRACTICE PROBLEMS for WEEK 9
1.
Since B is strictly dominated, it cannot be assigned positive probability at a Nash
equilibrium. Let p be the
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
ANSWERS TO PRACTICE PROBLEMS for WEEK 7
1.
(1) No, because the information set containing a is cfw_a,b,c which is not contained in E =
cfw_a,b,d,k,n.
(2
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
PRACTICE PROBLEMS for WEEK 10
T opic: incomplete information games
VERY IMPORTANT: do not look at the answers until you have made a VERY serious effort
122 Game Theory Professor Giacomo Bonanno
PRACTICE PROBLEMS for WEEK 9
T opic: mixed-strategy equilibria
VERY IMPORTANT: do not look at the answers until you have made a VERY serious effort to solve the problem. If you
turn to the answers to get clues or
122 Game Theory Professor Giacomo Bonanno
PRACTICE PROBLEMS for WEEK 7
T opic: information partitions, knowledge
and common knowledge
VERY IMPORTANT: do not look at the answers until you have made a VERY serious effort to solve the
problem. If you turn to
University of California, Davis - Department of Economics
ECON 122 : GAME THEORY
Professor Giacomo Bonanno
PRACTICE FOR FINAL EXAM
Answer all questions. Explain your answers.
1.
Consider the following game. There are two players. Each has to decide whethe
Professor Giacomo Bonanno
ECONOMICS 122 GAME THEORY
~
HOMEWORK # 5 ANSWERS
1. (a) The set of states is W = cfw_F, H, UF, PNS and, based on knowledge of the symptoms,
the information partitions are:
Mother
Roommate
Doctor
F
H
UF
PNS
F
H
UF
PNS
F
H
UF
PNS
(
18.1
Suppose there are three hunters named I, II, and III. In the scenario
described above, the set of strategies for all three hunters is the same,
but the payoff each hunter receives depends on the strategies of her
fellow hunters, as well as her own st
Test Form A
Instructions:
Enter your
ID number,
Test Form (listed on the top right of this page),
Name,
Subject (= Ecn 122), and
Date
on your Scantron form.
Choose the best answer among the possible answers given. You will have 80 minutes to
complete
Test Form D
Instructions:
Enter your
ID number,
Test Form (listed on the top right of this page),
Name,
Subject (= Ecn 122), and
Date
on your Scantron form.
Choose the best answer among the possible answers given. You will have 80 minutes to
complete
A little game to start with
Everybody picks a number between 0 and
100.
Introduction to Game Theory
The participant whose number is closest to
2/3 of the average wins $5 dollars.
ECN 122
Burkhard C. Schipper
The winner has to play the same game
against m