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GAB Bj 9 2. 1 0,0 Ai 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 that N = 20. Specifically, 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? Briefly explain why.Facehook or the new \"BETTER" version of Google Plus? Now consider a modication to the above story. Suppose that Google decide to make one last attempt to crack the social media market. Specically, 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 \"deciencies\" of Euro Wave and Google 1Wave. Everyone agrees that the resulting amendments are a weak improvement. In fact, a particular submt of the population now thinks Google Plus is the superior platform. However, despite the improvements, some people still prefer Facehook. The following makes this new story more precise: o 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 {3'} and Google Plus [3}. o The population is now split into two groups, A and B, and those in different groups have different preferences. Those in Group A prefer Facebook, while those in lGroup B prefer Google Plus. o Once each person has chosen an online plat-form, she interacts pairwise with every one else in the population, where the same platform is used with everyone. 1With two groups there are now three types of 25:? game: two A types interact via the game GM, two B types interact via the game GEE, while an A type interacts with a B type via GAB. The games are depicted below. Fayoffs are computed as before. 6'\" Sea A; 32 ,,.rn1slg,rll yam- (c) 15 marks Again with group sizes given as in part (b), suppose that the current strategy profile has all Group A individuals choosing Facebook and all Group B individuals choosing Google. . From this strategy profile, suppose one Group A individual decided to choose Google forever more. What would the resulting strategy profile be? . From this strategy profile, suppose one Group B individual decided to choose Facebook forever more. What would the resulting strategy profile 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 payoffs to reflect this