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Unformatted text preview: Problem Set 4 (Week of May 9) ECOS3012- Strategic Behavior, Semester 1, 2011 1. Work through all the end of chapter problems in the chapter “Backward Induction and Subgame Perfection” in Watson’s text. 2. (Stackelberg Competition) In a certain market with two firms, the price is P = 10- Q if the total output is Q ≤ 10 and equals 0 otherwise. The firms compete by choosing how much to produce in the following manner. Firm 1 is the leader and chooses her production first. Firm 2, the follower observes how much Firm 1 has produced and then selects her production. The marginal cost of production for both firms is zero. (a) Assuming that either firm can only choose her production to be only 2, 4 or 6, i. Draw the extensive form game. How many subgames are there? ii. What is the subgame perfect equilibrium? iii. Give a Nash equilibrium of this game that is not a subgame perfect equilibrium. (b) Now assume that either firm can choose any quantity continuously between 0 and 10. Write down the subgame perfect equilibrium. What quantity is produced? If a firm could choose, would it prefer to be a leader or a follower? 3. (Bargaining in Bilateral Monopoly.) A is a monopolist that uses an special input that only B produces to create a unique product. It turns out that if B offers input whose quality is q , which costs her c ( q ), A is able to sell her unique creation for R ( q ) where c ( · ) is a strictly increasing cost convex function and R ( · ) is a strictly increasing concave revenue function. Initially, take R ( q ) = √ q and c ( q ) = q 2 / 2. (a) Suppose the bargaining proceeds as a take-it-or-leave-it: B offers a to supply at unit price p , which A observes and chooses what q . (That is, having observed a price p , if A chooses q , she will pay B...
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- Spring '11
- Game Theory, Subgame perfect equilibrium