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Quiz Feedback | Social and Economic Networks: Models and Analysis
Feedback — Quiz Week 4
You submitted this quiz on Mon 3 Jun 2013 3:07 AM IST (UTC +0530). You got a
score of 35.00 out of 35.00.
Question 1
(Lecture 4.1)
Consider the undirected network represented in the picture.
Consider a symmetric version of the Connections Model with the following utility function
ui (g) = ∑
j≠i
and suppose
δ
l(i,j)
δ = 0.5
− ∑
j∈ N i (g)
and
c,
c = 0.4.
What is the utility of node 2, u2 (g) , in the pictured network?
Your Answer
3*0.5 + 0.25 - 3*0.4
✔
Score
Explanation
2.00
Correct
4*0.5 - 3*0.4
3*0.5 + 0.25 - 4*0.4
3*0.5 + 0.25 - 3*0.4 - 0.16
Total
2.00 / 2.00
Question 2
(Lecture 4.2)
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Consider a symmetric version of Connections Model with
of n
= 3
δ = 0.999
and
c = 1.4
and a society
people.
[Therefore the values are depicted in the picture.]
In which row(s) are the network(s) Pairwise stable?
Your Answer
Score
Explanation
a
✔
0.50
Incorrect
b
✔
0.50
Incorrect
c
✔
0.50
Incorrect
d
✔
0.50
Correct
Total
2.00 / 2.00
Question 3
(Lecture 4.2)
Consider a symmetric version of Connections Model with
of n
= 3
δ = 0.999
and
c = 1.4
and a society
people.
[Therefore the values are depicted in the picture.]
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Quiz Feedback | Social and Economic Networks: Models and Analysis
In which row(s) are the network(s) Pareto Efficient?
Your Answer
Score
Explanation
a
✔
0.50
Incorrect
b
✔
0.50
Correct
c
✔
0.50
Incorrect
d
✔
0.50
Correct
Total
2.00 / 2.00
Question 4
(Lecture 4.2)
Consider a symmetric version of the Connections Model with
society of n
= 3
δ = 0.999
and
c = 1.4
and a
people.
[Therefore the values are depicted in the picture.]
In which row(s) are the network(s) Efficient (maximizing the total sum of utilities)?
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Quiz Feedback | Social and Economic Networks: Models and Analysis
Your Answer
Score
Explanation
a
✔
0.50
Incorrect
b
✔
0.50
Correct
c
✔
0.50
Incorrect
d
✔
0.50
Incorrect
Total
2.00 / 2.00
Question 5
(Lecture 4.3)
Consider a symmetric version of the Connections Model in a society with
n = 5
people and
δ = 0.5 .
Which are the lower and upper bounds of the cost c, such that star networks are efficient?
Your Answer
Score
Explanation
0.25, 1
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0.5, 1
0.25, 0.5
✔
0.25, 0.875
Total
2.00
2.00 / 2.00
Question Explanation
The two bounds are
δ − δ
2
and
δ + (n − 2)δ
2
/2 ,
and so 0.25 and 0.875 in this question.
Question 6
(Lecture 4.4)
Consider a symmetric version of the Connections Model in a society with
δ = 0.5
and
n = 7
people and with
c = 1.
Which of the following describes the efficient network architectures?
Your Answer
Score
Explanation
The complete network
✔
Star networks involving all nodes
2.00
The empty network
None of the above
Total
2.00 / 2.00
Question Explanation
2
2
In this case, δ − δ = 0.25 and δ + (n − 2)δ /2
those two.
Therefore the star networks are (uniquely) efficient.
= 1.125 ,
and
c = 1
is in between of
Question 7
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(Lecture 4.5)
Consider a symmetric version of the Connections Model in a society with
n = 7
people and
δ = 0.5 .
For which of the following costs c is (are) star networks pairwise stable?
Your
Score
Explanation
Answer
0.2
✔
0.50
Incorrect. $$c
0.4
✔
0.50
Correct.
0.6
✔
0.50
Incorrect. c
> δ
is too high so that the central node has incentive
to delete any link.
0.8
✔
0.50
Incorrect. c
> δ
is too high so that the central node has incentive
to delete any link.
Total
2.00 /
2.00
Question Explanation
Star networks are pairwise stable if c is between
c=0.4 is a correct option.
δ − δ
2
= 0.25
and
δ = 0.5 .
Hence only
Question 8
(Lecture 4.6)
In the picture, consider adding a link 12 to the network g = {13, 24}. So the left network is g, and
the right network is g + 12. The number next to each node is the node's utility from that network.
Regarding the externality to node 3 brought by adding link 12, which of the following statements
is correct?
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Your Answer
Score
Explanation
1.00
Correct.
Adding link 12 has a positive externality on node 3.
Adding link 12 has a negative externality on node 3.
✔
Neither of the above.
Total
1.00 / 1.00
Question Explanation
Adding link 12 brings negative externality to node 3, since its utility from the network is reduced
by adding the link.
Question 9
(Lecture 4.6)
Consider the undirected network in the picture using "Coauthor" model (as described in this
video).
What is the utility of agent 1?
Your Answer
Score
Explanation
2.75
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3
3.5
4
✔
Total
2.00
2.00 / 2.00
Question Explanation
1's value = 1 + 1 + 1 + 1/2 + 1/2 = 4.
Question 10
(Lecture 4.7)
Consider undirected networks on 3 nodes, with the utilities of nodes depicted in the picture.
Choose the option that correctly answers the following two questions:
(1) In which row are the network(s) Efficient?
(2) In which row are the network(s) Pairwise stable?
Your Answer
Score
Explanation
(1) c, (2) b
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(1) c, (2) a
(1) b, (2) a
(1) b, (2) c
Total
✔
2.00
2.00 / 2.00
Question Explanation
Networks in row b are efficient, and networks in row c are pairwise stable.
Question 11
(Lecture 4.8)
In the pairwise stable structure of network(s) described in this video for Islands connections
model (Jackson&Rogers 2004), which of the following properties are correct?
Your Answer
Score
✔
0.50
✔
0.50
(Relatively) low diameter
✔
0.50
(Relatively) high clustering
✔
0.50
Average degree increases proportionally to the total number
Explanation
of nodes, as the number of islands goes up (fixing the number of
nodes in each island)
Diameter increases proportionally to the total number of
nodes, as the number of islands goes up (fixing the number of
nodes in each island)
Total
2.00 /
2.00
Question Explanation
The features of islands connections model include high clustering, low diameter, and regular
degree (which does not increase dramatically as the number of islands increase).
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Question 12
(Lecture 4.10)
Consider the networks with 3 nodes and the utilities as shown in the picture.
Which network(s) are Nash stable?
Your Answer
Score
a
✔
0.50
b
✔
0.50
c
✔
0.50
d
✔
0.50
Total
Explanation
2.00 / 2.00
Question Explanation
Networks a, c and d are all Nash stable.
Note that only network a is both pairwise stable and Nash stable, i.e. Pairwise Nash stable.
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Question 13
(Lecture 4.10)
Consider the networks with 3 nodes as shown in the picture.
Which network(s) are Pairwise Nash stable?
Your Answer
Score
a
✔
0.50
b
✔
0.50
c
✔
0.50
d
✔
0.50
Total
Explanation
2.00 / 2.00
Question Explanation
Network c is both Pairwise stable and Nash stable, so it is Pairwise Nash stable.
Network b is only Pairwise stable but not Nash stable.
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Question 14
(Lecture 4.11)
Consider connections model with
δ − δ
2
< c < δ , and the following process described by A.
Watts (2001):
a link is picked uniformly at random;
the link is added if that weakly benefits both players (at least one strictly);
the link is deleted if that strictly benefits either player;
go back to the first bullet point and repeat.
Which statement(s) are true?
[This is to guide you through the Proposition (A. Watts (2001)), as covered in this video.]
Your Answer
Score
Star networks involving all nodes are efficient.
✔
0.50
Star networks involving all nodes are pairwise stable.
✔
0.50
As the number of nodes n grows, the probability that the
✔
0.50
✔
0.50
Explanation
above process stops at a star network goes to 0.
When the above process reaches a star network with all
players, it may still move forward to other networks.
Total
2.00 /
2.00
Question Explanation
The first three statements are correct.
The last statement is incorrect: once a process hits a star, it will stop there.
Question 15
(Lecture 4.12)
Consider all undirected networks with 3 nodes as depicted in the picture.
In which row(s) are the network(s) Pairwise Nash stable?
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Your Answer
Score
a
✔
0.50
b
✔
0.50
c
✔
0.50
d
✔
0.50
Total
Explanation
2.00 / 2.00
Question Explanation
Networks a and d are both pairwise Nash stable.
Question 16
(Lecture 4.12)
Consider the discussion of improving paths with error
ϵ = 0.05
on networks with 3 nodes (as
described in this video, with utilities as a function of the network depicted in the picture).
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Starting from the green network in the middle of third row, what is the probability of staying at
the same network after one step?
Your Answer
Score
Explanation
2.00
Correct.
0
1
0.15
0.65
Total
✔
2.00 / 2.00
Question Explanation
Starting from the green network, there is a chance (1 − ϵ)/3 to move to the network with 3
links, and a chance ϵ/3 to move to either (upper left or right) networks with 1 link. Thus the
probability of staying is 1 − (1 − ϵ)/3 − 2ϵ/3 = (2 − ϵ)/3 = 0.65.
Question 17
(Lecture 4.13)
Consider a network formation game with directed networks on 2 nodes and with resulting utilities
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depicted in the picture as a function of the directed links formed (with arrows pointing from the
node that formed the link to the node at which it directed the link).
Which network(s) are the outcomes(s) of (pure) Nash equilibrium?
Your Answer
Score
a
✔
0.50
b
✔
0.50
c
✔
0.50
d
✔
0.50
Total
Explanation
2.00 / 2.00
Question Explanation
Both b and c are correct.
Question 18
(Lecture 4.13)
Consider the directed connections model with no decay (as described in this video).
What is the payoff to each nodes in the wheel network in the picture, with n=5 and c=3?
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Your Answer
Score
Explanation
3
1
✔
2.00
2
5
Total
2.00 / 2.00
Question Explanation
The payoff is 4 - 3 = 1.
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