The pencil market is controlled by two firms: AAA Pencil Company and BBB Manufacturing. The structure of the mark vered makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells of 14 pencils at the price for the duration of the period. There is very little brand loyalty among pencil buyers so that each stion firm's demand is highly elastic, Each firm's prices are thus very sensitive to inter-firm price differentials. The two firm must choose between a high and low price strategy for the coming period. Profits (measured in thousands of Rands) for the two firms under each price strategy are given in the payoff matrix below. AAA - low price AAA - high price BBB - low price 60, 60 250, -20 BBB - high price -20, 250 130, 130 A) Which firm has a dominant strategy? (2) What strategy should each firm follow? (2) BJ Assume that the game is to be played an infinite number of times. (Or, equivalently, Imagine that neither firm knows for certain when rounds of the game will end, so there is always a positive chance that another round is to be played after the present one.) Would the tit-for-tat strategy would be a reasonable choice? Explain this strategy. (6) () Assume that the game is to be played a very large (but finite) number of times. What is the appropriate strategy if both firms are always rational? (4)