2. In the classic Dr. Seuss tale The Sneetches, some Sneetches have stars on their bellies and others do not. Or, Seuss puts it: Now, the Star-Belly Sneetches Had bellies with stars. The Plain-Belly Sneetches Had none upon thars. The Star-Belly Sneetches are seen as superior because of their marking that makes them rarer than their plain-bellied neighbors. Suppose the population of Sneetches is N=200, and only 30 sneetches have stars. The payoffs to having a star or plain belly, as a function of the number of Sneetches with stars, n, are: Pstar(n) = 400-3n as the more Sneetches with stars, the less it is valued Pplain(n) = 50+ n, as the more star-bellies there are, the more a rare plain belly is more highly valued. a) Calculate current payoffs to show that being a Star-Belly sneetch is more highly valued. Sadly, there's nothing the plain-bellied sneetches can do to change their situation. Enter Sylvester McMonkey McBean with his amazing "star on" machine. Now plain-belly Sneetches can add a star. b) Assuming the "star on" machine is free to use, what is/are the Nash equilibrium(a) number of sneetches with stars? Show clearly how you find this.