Second Price Auction
Ichiro Obara
UCLA
November 25, 2013
Obara (UCLA)
Second Price Auction
November 25, 2013
1/1
Auction
Auction
Obara (UCLA)
Second Price Auction
November 25, 2013
2/1
Auction
Auction
So far we have studied only nonmonetary transactions.
Room Assignment
Ichiro Obara
UCLA
January 5, 2010
Obara (UCLA)
Room Assignment
January 5, 2010
1 / 46
General Introduction
General Introduction
Obara (UCLA)
Room Assignment
January 5, 2010
2 / 46
General Introduction
What will we learn in this course?
We
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
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
Assignment
Ichiro Obara
UCLA
September 26, 2013
Obara (UCLA)
Assignment
September 26, 2013
1 / 32
Assignment Problem
Assignment Problem
Obara (UCLA)
Assignment
September 26, 2013
2 / 32
Assignment Problem
Room Assignment Problem
Room Assignment Problem
Th
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
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
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
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: 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
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: 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: 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: 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 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
Random Serial Dictatorship
Ichiro Obara
UCLA
October 6, 2014
Obara (UCLA)
Random Serial Dictatorship
October 6, 2014
1 / 15
Random Serial Dictatorship
Random Serial Dictatorship
Obara (UCLA)
Random Serial Dictatorship
October 6, 2014
2 / 15
Random Serial
Matching
Ichiro Obara
UCLA
October 27, 2014
Obara (UCLA)
Matching
October 27, 2014
1 / 59
Matching Problem
Matching Problem
Obara (UCLA)
Matching
October 27, 2014
2 / 59
Matching Problem
Matching Problem
Three boys m1 , m2 , m3 and three girls w1 , w2 , w
Econ 145: Suggested Answer for Practice
Questions I
1. True or False? Are the following statements true or false? If you
think that they are true, explain why briey. If you think that they
are false, provide an explicit counterexample. The rst three quest
Second Price Auction
Ichiro Obara
UCLA
December 1, 2014
Obara (UCLA)
Second Price Auction
December 1, 2014
1 / 20
Auction
Auction
Obara (UCLA)
Second Price Auction
December 1, 2014
2 / 20
Auction
Auction
So far we have studied only nonmonetary transaction
ECON 145: Mathematical Economics
Problem Set II Solutions
1
Problem 1
Suppose that there are 5 patient-donor pairs (p1 ; d1 ) ; : : : ; (p5 ; d5 ) : Let ki be the kidney of donor i: Each patient has the
following "preference" over fk0 ; : : : ; k5 g (k0 i
ECON 145: Mathematical Economics
Problem Set I Solutions
1
Problem 1
Consider the following room assignment problem. There are 4 students and 4 rooms fh1 ; : : : ; h4 g : Room hi is initially
assigned to student i:
Suppose that the students have the follo
ECON 145: Mathematical Economics
Problem Set III Solutions
1
Problem 1
Consider a rst price auction with n bidders, whose values are independently and uniformly distributed over [0; 10] :
(a) Derive a symmetric Bayesian Nash equilibrium.
Note:
Notice that
ECON 145: Mathematical Economics
Problem Set IV Solutions: Revised
1
Problem 1
Consider the following linear programming problem.
maxx1 ;x2 f2x1 + x2 g
s:t: x1 + 3x2 4
x1 ; x2 0
(a) Find the dual problem of the Above primal problem
Answer:
Following the p
Econ 145: Problem Set I
Suggested Answer
May 6, 2011
1. Consider a general room assignment problem with N students and N rooms. Answer the following
questions.
(a) Suppose that the initial assignment of rooms is already ecient. Show that TTC algorithm lea
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 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
ECON 145 Quiz 1
Emre Girgin
UID:204-482-310
Problem 1. (a)
(h4 , h2 , h5 , h1 , h3 )
I used TTC to find the core allocation, as TTC gives the unique core allocation by Theorem 1&2 from thev
TTC lecture slide. On the first step, 1 wants to go to h4 , and 4
ECON 145 Quiz 2
Emre Girgin
UID:204-482-310
Problem 1. (a) At the first round s4 will go to p2 , the others will go to p1 . s1 , s2 will get into p1 and s4
will get into p2 .
At the second round s3 will get into p3 .
s2 , s1 p1 ,
s4 p2
s3 p3
This matching