Problem 1: [20 pts] Consider the following version of the location game discussed in lecture. Suppose instead that the nine regions are located on a circle as follows: 9 8 2 7 3 6 4 5 Two vendors simultaneously and independently select on which of the nine regions to locate. Suppose that there are 60 consumers in each region; each consumer will walk to the nearest vendor and purchase a soda, generating 1 dollar of profit for the vendor. If the vendors are equidistant from a region, then the vendors split those consumers in half. Part a: (10 pts) Determine the set of rationalizable strategies for each of the vendors. Part b: /10 pts) Find the set of all Nash equilibria of the above location game. Part c: [Extra Credit + 10) Now suppose that there are three vendors. Find all of the Nash equilibria of this game