Research on a large population

I have linked a better view of the question below
Now consider a modi cation to the above story. Suppose that Google decide to make
one last attempt to crack the social media market. Speci cally, they take on board
all the existing complaints about Facebook, and spend months working on the Google
Plus platform so that it is free of all the de ciencies” of Buzz Wave and Google Wave.
Everyone agrees that the resulting amendments are a weak improvement. In fact, a
particular subset of the population now thinks Google Plus is the superior platform.
However, despite the improvements, some people still prefer Facebook. The following
makes this new story more precise:
The entire population has N people. As before, each person chooses one social
media platform to exist on. The two available options remain the same: Facebook
(f) and Google Plus (g).
The population is now split into two groups, A and B, and those in di erent groups
have di erent preferences. Those in Group A prefer Facebook, while those in Group
B prefer Google Plus.
Once each person has chosen an online platform, she interacts pairwise with every-
one else in the population, where the same platform is used with everyone. With
two groups there are now three types of 2×2 game: two A types interact via the
game GAA, two B types interact via the game GBB, while an A type interacts with
a B type via GAB. The games are depicted below. Payo s are computed as before.
3. 40 marks Facebook or the new BETTER version of Google Plus?
Now consider a modification to the above story. Suppose that Google decide to make
one last attempt to crack the social media market. Specifically, they take on board
all the existing complaints about Facebook, and spend months amending the Google
Plus platform so that it is free of deficiencies. Everyone agrees that the resulting
amendments have not hurt the platform. In fact, a particular subset of the population
now thinks Google Plus is the superior platform. However, despite the improvements,
some people still prefer Facebook as before. The following makes this new story more
precise:
The entire population has 20 people. As before, each person chooses one social
media platform to exist on. The two available options are the same: Facebook (f)
and Google Plus (g).
The population is now split split into two groups, A and B, and those in dierent
groups have dierent preferences. Those in Group A prefer Facebook, while those
in Group B prefer Google Plus.
Once each person has chosen an online platform, he/she interacts pairwise with
everyone else in the population, where the same platform is used with everyone.
With two groups there are now three types of 2×2 game: two A types interact via
the game GAA, two B types interact via the game GBB, while an A type interacts
with a B type via GAB. The games are depicted below. Payos are computed as
before.
GAA GBB
A1
A2
f g
f 2, 2 0, 0
g 0, 0 1, 1
B1
B2
f g
f 1, 1 0, 0
g 0, 0 2, 2
GAB
Ai
Bj
f g
f 2, 1 0, 0
g 0, 0 1, 2
(a) 10 marks Classify the pure strategy Nash equilibria for this large population
game? Be careful as it may depend on the sizes of the two groups.
(b) 5 marks Suppose there are 12 Group A individuals and 8 Group B individuals.
What would you expect to be the most likely outcome of this game?
Page 3 of 5
(a) 10 marks Classify the pure strategy Nash equilibria for this large population
game? Be careful as it may depend on the sizes of the two groups.
(b) 5 marks Suppose that N = 20. Speci cally, suppose there are 12 Group A indi-
viduals and 8 Group B individuals. What would you expect to be the most likely
outcome of this game? Brie y explain why.
Page 3 of 5
(c) 15 marks Again with group sizes given as in part (b), suppose that the current
strategy pro le has all Group A individuals choosing Facebook and all Group B
individuals choosing Google.
From this strategy pro le, suppose one Group A individual decided to choose
Google forever more. What would the resulting strategy pro le be?
From this strategy pro le, suppose one Group B individual decided to choose
Facebook forever more. What would the resulting strategy pro le be?
(d) 5 marks Suppose that the Group B individuals are elitist and don’t want to be
seen as residing on the same platform as the `uncool’ Group A individuals. How
might you change the payo s to re ect this?