Networks: Fall 2014
David Easley and Jon Kleinberg
Homework 3 Solutions
(1) We know that in a second price auction bidding your true value is a dominant strategy that is, no matter
what the others do you are better o bidding truthfully. So the fact that b
1) a. First, for T1 the only possible values are that T1 offers 0 to S1 and sells to B1 for 1
because T1 has a monopoly over B1 and S1, and thus has complete control over them.
T2 also has a monopoly over S2, S3, and B2 since each are also only connected
Networks: Fall 2010
David Easley and Jon Kleinberg
Solution Set 5
(1) (a) In the book, we saw that if the rst two students guess blue, and the third student then
draws a red marble, then the conditional probability that the urn is majority-blue is 2/3, an
Networks: Fall 2012
David Easley and Eva Tardos
Practice Final Exam: solutions
December 1, 2013
Details of the nal exam are listed on handout with the questions. Here you get solutions,
and list of other topics to think about.
(1)
(a) Yes, U is dominant s
Networks: Fall 2014
David Easley and Jon Kleinberg
Homework 2 Solutions
(1a) The only pure Nash equilibrium here is (U, R). For any other strategy pair, there is a
player that benets from deviating.
(1b) The only pure Nash equilibrium here is (D, L). For
Usaamah Khan
UK45
1. Bidder 1 should bid his true value regardless of what the others bid. Truthful bidding is a
dominant strategy and it makes sense to bid your true value even if other bidders are
overbidding, underbidding or behaving in unpredictable w
Ji Soo Kim
Assignment 3
Econ 2040
September 28, 2013
1.
!
I should bid to my own value because if I bid more than my value (alternate bid),
and won, I could pay more than my value because bidder 2 and 3 could have had
higher value than my value. If I pay
Networks: Fall 2010
David Easley and Jon Kleinberg
Practice Midterm
The midterm is Wednesday, October 6, in class. It will be a closed-book, closed-notes
exam. The best guide to the coverage of the midterm is the contents of the course lectures up
through
1. (a) T1: It holds a monopoly over S1 and B1 since T1 is the only node connected to these two.
The flow of trade will from S1 to B1, and the profit T1 will get is 1-0=1. Bid price for S1 is 0,
ask price for B1 is 1.
T2: It holds a monopoly over S2, S3, a
Homework 6 Solutions
(1a) Let P r(BB ) be the probability that two blue balls are drawn. Then using Bayes Rule
we know that
P r(m B |BB ) =
P r(BB |mB )P r(mB )
P r(BB )
Since the probability of drawing one blue ball when the majority of the balls are blu
Networks: Spring 2010 David Easley and Jon Kleinberg
Practice Midterm February 26, 2010
The midterm is Monday, March 8, in class. It will be a closed-notes exam. The best guide to the coverage of the midterm is the contents of the course lectures up throu
Networks: Fall 2010
David Easley and Jon Kleinberg
Homework 5
Due November 12, 2010
As noted on the course home page, homework solutions must be submitted by upload to
the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you should write thes
Blog Post Number 2
Slap in the Facebook: It's Time for Social Networks to Open Up
http:/www.wired.com/software/webservices/news/2007/08/open_social_net Basically in this article, the author talks about how there are social networks all over the Inte
Homework 3 Solutions
(1) We know that in a second-price, sealed-bid auction that bidding your true value is a
dominant strategy. That is, no matter what the others do, you are better bidding
truthfully. So the fact that bidders 2 and 3 overbid does not ae
From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World.
By David Easley and Jon Kleinberg. Cambridge University Press, 2010.
Complete preprint on-line at http:/www.cs.cornell.edu/home/kleinber/networks-book/
Chapter 5
Positi
Networks: Fall 2015
David Easley & Jon Kleinberg
Homework 2
Due 11:15am, Friday, September 18, 2015
As noted on the course home page, homework solutions must be submitted by upload to the
CMS site, at https:/cms.csuglab.cornell.edu/. The le you upload mus
Networks: Fall 2013
Homework 3
David Easley and Eva Tardos Due at 11:15am, Monday, September 30, 2013
As noted on the course home page, homework solutions must be submitted by upload to
courses Blackboard site. The le you upload must be in PDF format. It
Networks: Fall 2014
David Easley and Jon Kleinberg
Homework 5 Solutions
(1a) By multiplying the click-through rate and advertisers valuations for each click, we obtain
advertisers valuations for slots
x
y
z
1 2 3
32 16 8
24 12 6
16 8 4
Running the procedu
Networks: Fall 2011
David Easley and Eva Tardos
Homework
Due before class on October 28, 2011
As noted on the course home page, homework solutions must be submitted by upload to the
CMS site, at https:/cms.csuglab.cornell.edu/. This means that you should
Networks: Fall 2015
David Easley and Jon Kleinberg
Homework 3 Solutions
(1) We know that in a second price auction bidding your true value is a dominant strategy that is, no matter
what the others do you are better o bidding truthfully. So the fact that b
Networks: Fall 2010
David Easley and Eva Tardos
Homework 5
Due November 11, 2011
As noted on the course home page, homework solutions must be submitted by upload to
the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you should write these
u
Networks: Spring 2010 David Easley and Jon Kleinberg
Homework 3 Due February 26, 2010
As noted on the course home page, homework solutions must be submitted by upload to the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you should write th
Networks: Fall 2010
David Easley and Eva Tardos
Homework 5
Due November 11, 2011
As noted on the course home page, homework solutions must be submitted by upload to
the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you should write these
u
Networks: Fall 2011 David Easley and Eva Tardos
Homework 3 Due before class on September 26, 2011
As noted on the course home page, homework solutions must be submitted by upload to the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you sho
Networks: Fall 2013
David Easley and Eva Tardos
Homework 4
Due at 11:15am, Friday, October 25, 2013
As noted on the course home page, homework solutions must be submitted by upload to courses
Blackboard site. The le you upload must be in PDF format. It is
Networks: Fall 2011 David Easley and Eva Tardos
Homework 2 Due in Class September 16, 2011
As noted on the course home page, homework solutions must be submitted by upload to the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you should wri
Networks: Fall 2011
David Easley and Eva Tardos
Homework 6
Due before class Wednesday, November 23
As noted on the course home page, homework solutions must be submitted by upload to
the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you sh
Networks: Fall 2010 David Easley and Jon Kleinberg
Homework 2 Due in Class September 17, 2010
As noted on the course home page, homework solutions must be submitted by upload to the CMS site, at https:/cms.csuglab.cornell.edu/. This means that you should
From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World.
By David Easley and Jon Kleinberg. Cambridge University Press, 2010.
Complete preprint on-line at http:/www.cs.cornell.edu/home/kleinber/networks-book/
Chapter 3
Strong
Ryan Sharkey
Problem Set 5
10/28/16
1.
a)
A
18 -> 7
9->-1
27->16
X
Y
Z
B
12 ->7
6->1
18->13
C
2
1
3
Price of a-11, b-5, and c-0 will be marketing clearing. At these prices X will get B, Y will get C, and Z will
get a.
b)
A
27
18
9
Z
X
Y
B
18
12
6
C
3
2
1
Ryan Sharkey
Networks Problem Set 7
1a.
1
1
3
(1 2 )(4 2 = 4)
41/2 4 = 3/4
41/2 4
3
=0
4
1
1 1 3
( 2 )( 2 ) = 0
4
4
Z = 1/16
Z = 9/16
Therefore the possible equilibrium points 0 , 1/16, 9/16
1b.
There are three regions to consider are below 1/16, between
Ryan Sharkey
Networks Problem set 8
1a)
5 will adopt behavior A
1b)
4 and 6 will give the best outcome for a cascade that will result in the adoption of behavior A.
1c)
You cant start with a single node because the two clusters have density two-thirds and
Ryan Sharkey
Networks Problem Set 3
1)
a) as bidder 1 you should only bid v1 because bidding your true value is always a dominant
strategy in second-price sealed auctions. By bidding your true value and winning you end up paying a
value below your true va
1)
a)
Bayes Theorem: P(A|B)=
P ( B| A ) P ( A )
P(B)
ProbabilityofA=havingthedisease;ProbabilityofB:testingpositive
ProbabilityofA=1/10,000=.0001
ProbabilityofB=(.0001)+(.1)=.1001
1(.0001)
.1001 =0.099%
b)
ProbabilityofAisnow.01
ProbabilityofBisnow.11
1(.