4. In the wars of attrition we discussed in class, the per-period cost of fighting was the same for each period. But in many situations, the cost of fighting rises as the contest continues. To examine such a situation, consider an alternating-decision war of attrition (with unlimited resources) between two firms, A and B, engaged in price war. A starts the game by deciding whether to quit or fight in the first round. If A fights, B decides whether to quit or fight in the second round, and so on. The game continues in this way until one of the players gives in. If one firm quits, the other firm takes over the market. The value of the market is W4 to A and W to B. The cost of fighting for A is 4 in the first round, 2c4 in the second round, and nc4 in the nt" round. Thus, the total cost of a price war ending after three round of fighting is 4 +2c4 +3c4 = 64. B's cost to fighting is similar, with cost p. Assume W, =21, 4 = 4, Wg = 10, and cg = 3 in parts (a)-(d). (a) Show the first six rounds of the game (A and B each move thrice). (b) If the firms only rely on credible threats and promises, what would be the last round in which each firm would fight, based on the increasing per-round cost? () What are the firms' equilibrium strategies for rounds 1-67? Give complete strategies. (d) Combining your answers, specify the equilibrium strategies in the full, infinite-length game. (e) What is the equilibrium path? Which firm will capture the market and why