Econ 145: Practice Questions I
1. True or False? Answer if the following statements about the standard room assignment problem (with n students initially endowed with
n rooms) are true or false. Explain why brie
y.
(a) Every individually rational allocati
PIC 10B Lecture 1 Winter 2014
Homework Assignment #3
Due Tuesday, February 4, 2014 by 5:00pm.
Objectives:
1. To redefine the Big 3: Copy constructor, Assignment operator, and
Destructor for a class whose objects manage heap memory.
2. To develop an applic
M151A - Applied Numerical Analysis
E. LIST 3
MATH 151A - Exercise List 3: Root Finding and Linear system.
The exercises marked with a star ( ) are due Wednesday, Nov 6th during lecture.
Exercise 1 The equation x ln(x) 2 = 0 has a unique zero, , in the int
Room Assignment
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General Introduction
General Introduction
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General Introduction
What will we learn in this course?
We
Econ 145: Practice Questions I
Suggested Answer February 8, 2010
1. Consider a room assignment problem with 4 students and 4 rooms cfw_h1 , . . . , h4 . Room hi is initially assigned to student i. Suppose that the preferences of the students are as follo
Assignment
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Assignment Problem
Assignment Problem
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Assignment Problem
Room Assignment Problem
Room Assignment Problem
Th
Econ 145: Suggested Answer for Practice
Questions II
1. Matching Consider the following matching
and women.
w1
w2
m1
m1
w3
w1
m2
m2
w1
w2
m3
m3
m1
m2
w1
w1
m2
m1
w2
w2
m1
m3
w3
w3
problem with three men
w3
w2
w3
m3
m3
m2
(a) Apply the deferred acceptance
Econ 145: Suggested Answer for Practice
Questions I
Use any theorem from the lecture slides without proving it again, but
mention clearly which theorem you are using when you do so.
1. True or False? Are the following statements are true or false. If you
Econ 145: Midterm Exam
Suggested Answer
February 16, 2010
1. (30 pts.) Consider a room assignment problem with 3 students and 3 rooms cfw_h1 , . . . , h3 . Room hi is
initially assigned to student i. Suppose that the preferences of the students are as fo
Econ 145: Practice Questions II
Ichiro Obara March 11, 2010
1. Consider the second price auction with three bidders. (a) If (v1 , v2 , v3 ) = (0.5, 0.7, 0, 2) , who wins and pays how much? (b) Compute the expected revenue for the seller in dominant strate
ECON 145: Mathematical Economics
Final Exam Answers
1
Problem 1 (30 pts)
Suppose that there are n buyers, whose values of a good follow (independent) uniform distribution on [0; 1] : Answer the
following questions.
(a) Suppose that a seller run a rst pric
Econ 145: Suggested Answer for Practice Questions II
Ichiro Obara March 13, 2010
1. Consider the second price auction with three bidders. (a) If (v1 , v2 , v3 ) = (0.5, 0.7, 0, 2) , who wins and pays how much? Answer. Bidder 2 wins and pays 0.5. (b) Compu
Econ 145: Practice Questions I
Ichiro Obara
1. Room Assignment Consider the room assignment problem with 3
students and 3 rooms fh1 ; :; h3 g: Room hi is initially assigned to
student i: Answer the following questions.
(a) Suppose that every student prefe
Econ 145: Suggested Answer for Practice
Questions II
Ichiro Obara
1. School Choice Problem. Consider a matching problem between
two schools p1 ; p2 and 10 students. Student si prefers p1 to p2 for
i = 2; 4; 6; 8; 10 and prefers p2 to p1 for i = 1; 3; 5; 7
School Choice
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UCLA
November 17, 2014
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School Choice
November 17, 2014
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Boston Public School Match
Boston Public School Match
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Boston Public School Match
Boston Mechanism
Bos
Quiz 1
Marc A Jimenez
Economics 145: Mathematical Economics
April 20, 2015
Exercise 1. Find all core allocations. Describe how you nd them step by step. Also,
explain why there is no other core allocation.
Solution. We can apply TTC algorithm to nd the un
Econ 145: Problem Set IV
Suggested Answer
March 12, 2010
1. (A.15-1, SSS) You are one of n bidders who draw i.i.d. valuations from F (x). The probability that your
draw x is the highest is F (x)n1 . Then what is the probability that your draw is k th high
Econ 145: Problem Set III
Suggested Answer
March 11, 2010
1. Many-to-One Matching Suppose that there are 4 workers w1 , ., w4 and 2 rms f1 , f2 with
capacity q1 = q2 = 2. Their preferences are as follows.
w1
w2
f1
f2
w4
w3
f1
f2
w3
w4
f1
f2
w2 , f 2
w1 ,
Econ 145: Suggested Answer for Practice
Questions II
Use any theorem from the lecture slides without proving it again, but
mention clearly which theorem you are using when you do so.
1. School Choice Consider the standard model of school choice. It is
a s
Suggested Answer for Quiz II
Ichiro Obara
1. (50 pts) Consider a matching problem between two schools p1 ; p2 and
6 students. Student si prefers p1 to p2 for i = 2; 4; 6 and prefers p2
to p1 for i = 1; 3; 5: Students can be divided into three groups: G1 =
Econ 145: Suggested Answer for Practice
Questions I
1. True or False? Answer if the following statements about the standard room assignment problem (with n students initially endowed with
n rooms) are true or false. Explain why briey.
(a) Every individual
Econ 145: Practice Questions III
1. School Choice I Consider a matching problem between two schools
p1 ; p2 and 10 students. Student si ; i = 2; 4; 6; 8; 10 prefer p1 to p2 and
student si ; i = 1; 3; 5; 7; 9 prefer p2 to p1 : Students are divided into two
Econ 145: Suggested Answer for Practice
Questions II
1. Matching Consider the following matching
and women.
w1
w2
m1
m1
w3
w1
m2
m2
w1
w2
m3
m3
m1
m2
w1
w1
m2
m1
w2
w2
m1
m3
w3
w3
problem with three men
w3
w2
w3
m3
m3
m2
(a) Apply the deferred acceptance
Second Price Auction
Ichiro Obara
UCLA
December 1, 2014
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December 1, 2014
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Auction
Auction
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Second Price Auction
December 1, 2014
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Auction
Auction
So far we have studied only nonmonetary transaction
Econ 145: Suggested Answer for Practice
Questions III
1. School Choice I Consider a matching problem between two schools
p1 ; p2 and 10 students. Student si ; i = 2; 4; 6; 8; 10 prefer p1 to p2 and
student si ; i = 1; 3; 5; 7; 9 prefer p2 to p1 : Students
Matching
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October 27, 2014
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Matching Problem
Matching Problem
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Matching Problem
Matching Problem
Three boys m1 , m2 , m3 and three girls w1 , w2 , w
Random Serial Dictatorship
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October 6, 2014
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Random Serial Dictatorship
Random Serial Dictatorship
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Random Serial
Econ 145: Suggested Answer for Midterm Exam
November 3, 2016
1. (35 pts.) Are the following statements about one-to-one matching true
or false? If you think that a statement is true, explain why briey.
If you think that it is false, nd an explicit counter
Econ145: Suggested Answer for Quiz II
December 2, 2016
1. School Choice (30 pts.) Consider a matching problem between three
schools p1 ; p2 ; p3 and 4 students s1 ; :; s4 . Except for s4 ; every student has the following preference p1 si p2 si p3 : s4 s p
Econ 145: Suggested Answer for Practice
Questions II
1. School Choice: True and False Consider the standard model of
school choice. It is a special type of many-to-one matching model
where each schools preference (i.e. priority class) is not strict and
ev
Quiz II
November 19, 2016
Due on December 1, 2016
You may work on your own or belong to one and only one group (which does
not need to be the same as your previous group). Each groups answer needs to
state clearly who are the members of the group. The max
Econ 145: Practice Questions II
1. School Choice: True and False Consider the standard model of
school choice. It is a special type of many-to-one matching model
where each schools preference (i.e. priority class) is not strict and
every student is accept