QUESTION 1 Two stores (store 1 and store 2) in your hometown are competing to increase their respective market shares. There are currently 200 000 people in your home town, and 80 000 of them do their shopping at store 1. In each period, store 1 customers have an 85% chance of returning, and 15% of them switching to store 2. Meanwhile, store 2 customers have 95% chance of returning, and 5% switching to store 1. a) Set up both the vector of state probabilities and the matrix of transition probabilities b) Find the states of probabilities of the next period. c) Find the states of probabilities of two periods from now. d) Find the equilibrium conditions and explain what it means. QUESTION 2 Consider the 2 x 3 payoff matrix below: Y1 Y2 Y3 X1 86 42 200 X2 36 106 155 a) Can the players of the above game develop a pure game strategy? Why? (3) b) What are the ultimate strategies of each player? (8) c) What is the value of the game? (2) d) Which player would you like to be? (2) QUESTION 3 A group of businessmen in South Africa is considering the construction of a private clinic. In doing so they can either build a big clinic (offering multiply services) or a small specialized clinic. If the medical demand is high (favorable market for the clinic), the businessmen could realize a net profit of R1000 000 for a big clinic or R200 000 with a small clinic. If the market is not favorable, they could loss R500 000 with a large clinic and R90 000 with a small clinic. Of course, they dont have to proceed at all, in which case there is no cost. In the absence of any market data, the best the businessmen can guess is that there is a 50-50 chance the clinic will be successful. Moreover, the businessmen have been approached by a market research firm that offers to perform a study of the market at a fee of R50 000. The market researchers claim their experience enables them to use Bayess theorem to make the following statements of probability: Probability of a favorable market given a favorable study = 0.82 Probability of a favorable market given an unfavorable study = 0.11 Probability of a favorable study = 0.55. a) Set up the decision tables with probabilities. b) Draw the decision tree of this complex situation. c) Compute the EMV at each node. d) What do you recommend?