Consider a location game with five regions on the beach in which a ven- dor can locate. The regions are arranged on a straight line, as in the origi- nal game discussed in the text. Instead of there being two vendors, as with the original game, suppose there are three vendors who simultaneously and independently select on which of the five regions to locate. There are thirty consumers in each of the five regions; each consumer will walk to the nearest vendor and purchase a soda, generating a $1.00 profit for the vendor. Assume that if some consumers are the same distance from the two or three nearest vendors, then these consumers are split equally between these vendors. (a) Can you rationalize the strategy of locating in region 1? (b) If your answer to part (a) is “yes,” describe a belief that makes locating at region 1 a best response. If your answer is “no,” find a strategy that strictly dominates playing strategy 1.