(e) Give the matrix representations for the four information sets in the part (c) game,

namely h1 (where the Incumbent learns that its the strong type), h2 (where the Incumbent learns that its the weak type), h3 (where the Competitor learns about the

price reduction of $2), and h4 (where the Competitor learns that there is no price reduction). For simplicity, you only need to give the payoffs of the player who is active

in that information set, just like what we did in the slides.

(f) For each round of elimination, clearly state which strategies are eliminated, how they

are strict dominated, and in which information set are they dominated. (You should

only eliminate the strictly dominated actions but not the weakly dominated actions.)

(g) What are the strategy profiles surviving ICD?

Problem 2. Consider a market that is dominated by a monopoly (the Incumbent). A new firm (the Competitor) is considering to enter the market. There could be two types of the Incumbent, the strong type and the weak type. The probabilities of the Incumbent being strong and weak are both 0.5. The true type of the Incumbent is unknown to the Competitor. If the Incumbent is strong, the Competitor will lose badly in the price war if it enters the market. In this case, the Incumbent's payoff is 5 and the Competitor gets -1. If the Incumbent is weak, it will have to share the market with the Competitor if the Competitor enters the market. In this case, the Incumbent's payoff is 3 and the Competitor also gets 3. If the the Competitor doesn't enter the market, its payoff would be 0. And the Incum- bent, strong or weak, gets 10 by holding its monopoly position in the market. Problem 2. Consider a market that is dominated by a monopoly (the Incumbent). A new firm (the Competitor) is considering to enter the market. There could be two types of the Incumbent, the strong type and the weak type. The probabilities of the Incumbent being strong and weak are both 0.5. The true type of the Incumbent is unknown to the Competitor. If the Incumbent is strong, the Competitor will lose badly in the price war if it enters the market. In this case, the Incumbent's payoff is 5 and the Competitor gets -1. If the Incumbent is weak, it will have to share the market with the Competitor if the Competitor enters the market. In this case, the Incumbent's payoff is 3 and the Competitor also gets 3. If the the Competitor doesn't enter the market, its payoff would be 0. And the Incum- bent, strong or weak, gets 10 by holding its monopoly position in the market