SOLUTION: 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

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 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, 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. Payo↵s 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.