# Social Networks | NPTEL | Week 7 Assignment Solutions

This set of MCQ(multiple choice questions) focuses on the Social Networks NPTEL Week 7 Assignment Solutions.

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### Social Networks NPTEL 2022 Week 7 Assignment Solutions

Q1. Assume that the actions AA and BB yield every player a payoff of aa and bb. Further assume that there are two friends Ram and Shyam; Ram decides to adopt action AA while Shyam decides to adopt action BB. What are the payoffs that they get?

a) Ram- a, Shyam- b
b) Ram- a, Shyam- 0
c) Ram- 0, Shyam- b
d) Ram- 0, Shyam- 0

Q2. Consider a set of initial adopters of behavior A, with a threshold of q for nodes in the remaining network to adopt behavior AA. Given the following two statements,
Statement 1: If the remaining network contains a cluster of density greater than 1−q, then the set of initial adopters will not cause a complete cascade.
Statement 2: Whenever a set of initial adopters does not cause a complete cascade with threshold q, the remaining network must contain a cluster of density greater than 1−q.
Choose the correct option from the following.

a) Both Statement 1 and Statement 2 are true.
b) Both Statement 1 and Statement 2 are false.
c) Statement 1 is true but Statement 2 is false.
d) Statement 2 is true but Statement 1 is false.

Q3. Consider two actions A and B. The payoff associated with the action A is 30 while the payoff associated with action B is 10. In such a case, what is the threshold fraction of neighbors that should have adopted A, in order for a node to adopt the action A?

a) 1/3
b) 1/4
c) 1/5
d) 1/3

Q4. Given a node X having 8 friends/neighbors. 3 of its neighbors have decided to adopt the behavior/action A having a payoff of 11. 5 of its friends have adopted the action B yielding a payoff of 6. What is the payoff X gets from its friends who have adopted B?

a) 30
b) 40
c) 10
d) 6

Q5. In the network shown in Figure 2, what is the density of the cluster comprised by the set of nodes {1, 2, 3, 4}?

a) 1/3
b) 1/2
c) 3/2
d) 2/3

Social Networks NPTEL Week 7 Assignment Solutions

Q6. Given a network as shown in Figure 3. Assume that initially every node in this network has adopted behavior B. Next, a new behavior A is introduced in the network and the nodes v and w are the initial adopters of this behavior A, i.e., nodes v and w now have adopted behavior A and rest of the nodes have adopted behavior B. The payoff associated with A is a=3 and the payoff associated with B is b=2. After the introduction of this new behavior A in the network, all the nodes will start weighing their options and might change their behavior. This leads to a cascade in the network. After two iterations, which nodes would have adopted the behavior A?

a) v, w, r
b) v, w, t, s
c) v, w, r, s, t
d) v, w, r, s, t, u

Q7. Let v be a node in a graph. Suppose that a pp fraction of v′s neighbors have behavior A, and a (1−p) fraction have behavior B; that is, if v has d neighbors, then pd adopt A and (1−p)d adopt B, as shown in Figure 5. Behavior A has a payoff of a and behavior B has a payoff of b. Then A is a better choice for v if

a) p ≥ a / b
b) p ≥ b / a
c) p ≥ a / a+b
d) p ≥ b / a+b

Social Networks NPTEL Week 7 Assignment Solutions

Q8. Given a network as shown in Figure 6. Assume that initially every node in this network has adopted behavior B. Next, a new behavior A is introduced in the network and the nodes 1 and 3 are the initial adopters of this behavior A, i.e., nodes 1 and 3 now has adopted behavior A and rest of the nodes have adopted behavior B. The payoff associated with A is a=3 and the payoff associated with B is b=1. After the introduction of this new behavior A in the network, all the nodes will start weighing their options and might change their behavior. This leads to a cascade in the network. When the cascade ends, which all are the nodes who have adopted the behavior A.

a) 1, 3, 2
b) 1, 3, 2, 4
c) 1, 3, 2, 4, 7
d) 1, 3, 2, 4, 5, 6, 7, 8

Social Networks NPTEL week 7 Assignment Solutions

Q9. Consider a group of 10 bachelors, 5 live on the first floor of the apartment and 5 live on the second floor. Suppose that each person in this group has two friends on their own floor, and one friend on the other floor. Now, a new restaurant opens, and five persons all living on the first floor each begin eating there on the first day. This action will eventually be adopted by

a) Nobody in the apartment
b) Only the bachelors on the first floor
c) Only the bachelors on the second floor
d) Can’t say

Q10. Consider the following network with green nodes following the action A and red nodes following the action B at Time t = 1 (Figure 7).
The payoff for action A is 6 and for B it is 5. Each one in this network changes his/her action based on his/her friends actions. What will happen after one complete iteration.

a) All nodes adopt action A
b) All nodes adopt action B
c) Some nodes adopt action A and other nodes adopt action B
d) Insufficient data

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