- In the internet era, many individuals are concerned about their privacy but they also value benefits from online interactions. Every individual likes others to share their data, as this improves applications, but they would rather keep their data private. Let x = 0, 1 denote the action to share data online (e.g. post photos in Instagram) for every member of society. The utility function is u(x) = jij - ax; (i.e. each i enjoys when other individuals, j share data but dislike when they do so xi). (a) Argue that if a < N-1, where N is the size of the population, it is efficient for everyone to join. Can you describe the set of efficient allocations for a = 2 and N = 4? (b) Suppose that every individual chooses on their own. Show that they will not share any data as long as a > 0. Is this efficient? (c) The platform now makes it so that to access other people's data, you need to share your own. Write down a utility function that is consistent with this situation (notice that u(x) = 0 if x = 0). Show that every individual shares their data provided that a < N - 1.