AM STUCK

(2. Consider the relaxed monopol}r prisingproblem {HP} in which only the following down- ward adjacent incentive constraints (EMU) and a participation constraint (PG) for type t' = D are imposed. g I}: 2;- Hg p1, {BEIGE} HIF n 2 er a], {DAICIJ ux/$ lit 2 '3' {PG} Show that all these eonstramta bind in a solution to this relaxed problem. d. Show that if the solution obtained in the relaxed problem (HP) satises monotoniclty, i.e. a; 2 a"; 1';- a, then all of the inoentive constraints and participation constraints in the original problem are satised and the solution to the relaxed problem is also a solution to the original problem. e. Solve the relaxed problem [HP]. Compare the optimal quality levels [ageing] to the quality levels the monopolist would choose in part a. Discuss any dierenoee. 1'. Based on the solution to (HP) in part e, provide a sufcient condition on buyers' preferences such that the solution to [HP] in part e is indeed a solution to the original problem in part b. Interpret this condition. ls the monopoly better off when this condition holds than when a solution to {HP} is not a solution to the original problem in part b? 4. A monopoly rm I knows that rm E is considering entering its market and knows that the product design team at rm E is either good {G} or had {13]. Firm I initially believes that the design team is more likely good than had. Firm E knows the quality of its design team. If E decides to enter the market, it can do so with either a high or low investment. If the iuvmtment is high and the design team is good, then E's product quality is high. If the investment is low and the design team is bad, the product quality is low. The product quality is medium if either the investment is high and the design team is bad or else if the investment is low and the design team is good. Firm I can see the quality of E 's product (high, medium, or low), but does not directly know the quaiity of E's design team before deciding whether to ght or accommodate E in the market. If E stays out of the market, its payoff is I} and Fe is 5. The two tables below show the payos to E and I, depending on their decisions, when E enters the market. The left table shows the payos when E's design team is good and right tahle shows the payoffs if the team is had. The structure of this interaction is common knowledge to E and I. a The interaction between E and I can be represented by a game with the tree above. \"hitting on this sheet, label the moves, the players that move them, and the payofa in the tree above. (Turn in this sheet with your bluebook.) Explain briey how you can teli which player moves in which information set. b. Explain how you can tell that the decisions represented in the tables above are not the players" pure strategies. List all of E's pure strategies in the game. c. How many pure strategies does I have in the game? Give examples of two of them. {1. Does E have any weakly dominated strategies in the game? If so nd one. e. Find every sequential equilihrium {SE} in which I plays a pure strategy. Justify your answer. Ehrplain what the outcomes SE are and discuss whether they are plausible. Is there an SE in which I can detect for sure whether or not E's design team is good? f. Is there a Nash equilibrium {NE} in which E chooses not to enter the market no matter what? If so, discuss the plausibility of this outcome. If not, explain why not