Social Networks | Week 7

Social Networks Week 7 Assignment 7 Answers

Course Link: Social Networks | Week 7

Q1. A cascade cannot be complete in a network with threshold of adoption = q, if there exist a cluster with density
lesser than q
greater tan q
lesser than (1 – q)
greater than (1 – q)

Q2. Let ‘x’ be a node in a graph. Suppose that a ‘p’ fraction of the neighbors of ‘x’ have behavior A, and a (1 – p) fraction have behavior B; that is, if ‘x’ has ‘d’ neighbors, then pd adopt A and (1- p)d adopt B, as shown in the following Figure. Behavior A has a payoff of ‘a’ and behavior B has a payoff of ‘b’. Then A is a better choice for ‘x’ if
p ≥ a/b
p ≥ b/a
p ≥ a/(a + b)
p ≥ b/(a + b)

Q3. Find the cluster density of the blue color nodes shown in the given figure 14.
1/2
2/3
3/4
3/5

Q4. Which of the following are valid factors for influence diffusion?
Payoff
Key people
Both Payoff and key people
Neither Payoff nor key people

Q5. Consider the basic coordination based game theoretical model for cascading behavior. The payoffs associated with behaviours ‘A’ and ‘B’ are a and b respectively. Consider two friends x and y adopting behaviours ‘A’ and ‘B’ respectively. Assuming that x and y have no other friends than each other, the total payoff which they receive is
ab
a + b
a/b
b/(a + b)

Q6. Given a network as shown in the following Figure, 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 have adopted behavior A and the 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. When the cascade ends, which all are the nodes who have adopted the behavior A.
1, 3, 2
1, 3, 2, 4
1, 3, 2, 4, 5
1, 3

Q7. Let us consider a model for collective action shown in Figure 16, where the intrinsic threshold is given for every node. Which of the following statements is INCORRECT for this case?
you will go for a protest as it has two neighbors, and its threshold is two.
we will not go for a protest because w has a threshold of 4 and there are only two other nodes in the network.
we will not go for a protest because its threshold is 4 and there are only two neighbors
all three nodes will go for a protest as the average threshold is 3 and there are three nodes in the network

Q8. Given a node X having 10 friends/neighbors. 3 of its neighbors have decided to adopt the behavior/action A having a payoff of 12 while 7 of its friends have adopted the action B yielding a payoff of 9. What is (i) the payoff that X gets from its friends who have adopted the action A, (ii) the payoff that X gets from its friends who have adopted B, (iii) The final action/behavior adopted by X?
(i) 36 ,(ii) 63, (iii) B
(i) 63 ,(ii) 36, (iii) B
(i) 36 ,(ii) 63, (iii) A
(i) 63 ,(ii) 36, (iii) A

Q9. Consider the social network in the Figure 17, and again let’s suppose that in the A-B coordination game. Initially, all nodes have adopted B. There are two initial adopters node 7 and 8 for A. we have a payoff of a = 3 and b = 2, what is the threshold for any node to switch from B to A?
2/3
3/2
2/5
3/5

Q10. For the A-B coordination Game mentioned in Question 9, What are the nodes that have adopted action A after the next three steps?
nodes 5 to 10
nodes 4 to 10
nodes 4 to 17
all nodes 1 to 17