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
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
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.
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 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
Professor Giacomo Bonanno
ECONOMICS 122 GAME THEORY
~
HOMEWORK # 2 ANSWERS
1. (a) The preferences are as follows:
Preferences of a MALE:
outcome utility
Preferences of a FEMALE:
outcome utility
MF
MFF
all
5
4
3
MF
MMF
all
5
4
3
MMF
MM
2
1
MFF
FF
2
1
alone
University of California, Davis - Department of Economics
Professor Giacomo Bonanno
ECN 122 : Game Theory
WINTER 2017 - THIRD MIDTERM EXAM
Version 1
Answer all questions. If you dont explain (= show your work for) your answers you will get no credit.
NAME
University of California, Davis - Department of Economics
Professor Giacomo Bonanno
ECN 122 : Game Theory
WINTER 2017 - SECOND MIDTERM EXAM
Version 1
Answer all questions. If you dont explain your answers you will get no credit.
NAME:_ University ID:_
CIR
University of California, Davis - Department of Economics
ECN 122 : Game Theory
Professor Giacomo Bonanno
Winter 2017 - FIRST MIDTERM EXAM
Version 2
Answer all questions. Explain your answers.
NAME:_ University ID:_
By writing your name on this exam you c
University of California, Davis - Department of Economics
Professor Giacomo Bonanno
ECN 122 : Game Theory
WINTER 2017 - THIRD MIDTERM EXAM
Version 2
Answer all questions. If you dont explain (= show your work for) your answers you will get no credit.
NAME
University of California, Davis - Department of Economics
Professor Giacomo Bonanno
ECN 122 : Game Theory
WINTER 2017 - FINAL EXAM
Version 2
Answer all questions. If you dont explain your answers you will get no credit.
NAME:_ University ID:_
CIRCLE THE N
University of California, Davis - Department of Economics
Professor Giacomo Bonanno
ECN 122 : Game Theory
WINTER 2017 - FINAL EXAM
Version 1
Answer all questions. If you dont explain your answers you will get no credit.
NAME:_ University ID:_
CIRCLE THE N
University of California, Davis - Department of Economics
ECN 122 : Game Theory Professor Giacomo Bonanno
Winter 2017 - FIRST MIDTERM EXAM
Version 1
Answer all questions. Explain your answers.
NAME:_ University ID:_
By writing your name on this exam you c
ECN 122 : Game Theory
Professor Giacomo Bonanno
WINTER 2017 - THIRD MIDTERM EXAM: ANSWERS for VERSION 1
1. (a) The extensive form is as follows:
NATURE
1/5
1
4/5
L
A
1
R
B
A
B
2
C
z1
z1
0
85
C
D
z3
z3
z4
z4
z5
z1
1
85
0.5
0
0.85
85
D
z2
z2
0
100
C
C
D
z6
University of California, Davis - Department of Economics
Professor Giacomo Bonanno
ECN 122 : Game Theory
WINTER 2017 - SECOND MIDTERM EXAM
Version 2
Answer all questions. If you dont explain your answers you will get no credit.
NAME:_ University ID:_
CIR
ECN 122 : Game Theory
Professor Giacomo Bonanno
WINTER 2017 - FINAL EXAM: ANSWERS for VERSION 2
1. (a) The prisoner is Dan; he claims correctly that his hat is yellow and he reasons as
follows:
if my (=Dans) hat were red, then Bill would see it and reason
Professor Giacomo Bonanno
ECONOMICS 122 GAME THEORY
~
HOMEWORK # 5 ANSWERS
a
(a) Describe the state by three numbers b where a is the sum of money that Pete put in
c
the envelope, b is the sum of money given to Andrea and c is the sum of money given t
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 6 (for due date see web page)
Consider the following situation of two-sided incomplete information:
G1
G2
1:
a
2:
a
1
3
1
2
b
1
2
1
2
G1
1
2
ECONOMICS 122 GAME THEORY
Professor Giacomo Bonanno
~
HOMEWORK # 6 ANSWERS
(a) Let p be the probability of T and q the probability of L. Then p and q are given by the
solution to q 2(1 q ) and 4(1 p ) 2 p 1 p , which is q
2
3
and p 53 . Thus
T B L R
the
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 # 4 ANSWERS
1. The strategic form is as follows
2
1
R
M
l
2,0
4,0
r
2,0
4 , 1
L
1 ,1
1,0
The Nash equilibria are: pure-strategy: (R,r)
r
R M L l
mixed-strategy:
1 0 0 q 1 q
for every q suc
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
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
Elias, Tsakas
www.elias-tsakas.com/teaching/ecn122.htm
Game theory: A branch of applied mathematics, which we use to study (strategies) interaction
Set theory
Union of two sections
What complementary
Probability, Expected values
Functions, maximiz
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 4 (for due date see web page)
1.
Find all the Nash equilibria, including mixed-strategy equilibria, of the following game.
1
R
x0
2
0
M
L
x1
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 5 (for due date see web page)
Pete and his three daughters Elise, Andrea and Theresa are in the same room. Pete
gives a sealed envelope to El
Department of Economics, University of California, Davis
Ecn 122 Game Theory Professor Giacomo Bonanno
HOMEWORK # 3 (for due date see web page)
1. Consider the following game. The players are TA1 (Teaching Assistant 1), TA2 (Teaching
Assistant 2) and IRS