3. Facebook 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 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: 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 (f) and Google Plus (9). c 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 Group B prefer Google Plus. 0 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 2x2 game: two A types interact via the game GAA, two B types interact via the game G33, while an A type interacts with a B type via GAB. The games are depicted below. Payoffs are computed as before. (a) 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) Suppose that N = 20. Specically, suppose there are 12 Group A indi- viduals and 8 Group .8 individuals. What would you expect to be the most likely outcome of this game? Briey explain why