Problem II - Textbook Exercise 16.6.1 (2 points) Consider the game in Table 16.6.2, "A Variation of the Price Cutting Game" and consider a strategy in which firm 1 prices high in odd numbered periods, and low in even numbered periods, while 2 prices high in even numbered periods, low in odd numbered periods. If either deviate from these strategies, both price low from then on. Let & be the discount factor. A player gets a payoff from each stage game, so her total payoff from the supergame is the discounted sum of the payoffs from each stage game. The discounted sum of a player's payoffs from a repeated game is a geometric series. Since Firm 1 starts the sequence by pricing Low, its stream of payoffs is (25, 0, 25, 0, ..). At a discount rate of & per period, the present value of this stream of payoffs II, is IT: = 25 (1 + 87 +6'+...) = 141 = 7 9) [(1 = 25/(1-5%2) ] which is obtained by applying the formula for an infinite geometric series. Since Firm 2 starts the sequence by pricing High, its stream of payoffs is (0, 25, 0, 25, ..). At a discount rate of & per period, the present value of this stream of payoffs II, is I12 = 25 (8 + 87 + 8+...) = 112 = -256 [12 = 256/(1-8*2) ] which is obtained by applying the formula for an infinite geometric series. In any period, the firm whose turn is to price High will have the greater incentive to deviate from the alternating strategy. For instance, this is the dilemma faced by Firm 2 in Round 1. (i) Show that the alternating strategy from each firm's assigned role per turn is sustainable if 8 2 1/4. [Hint: compute and compare the present value of the infinite stream of payoffs from defection to that of the alternating strategy]