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Simon Fraser University Fall 2014 Econ 302 (D100) Quiz Instructor: Songzi Du Thursday October 2 2014, 8:30 – 9:20 AM Write your name, SFU ID number, and tutorial section number both on the exam booklets and on the questionnaire. Hand in both the exam booklets and this questionnaire. But note that only the exam booklets are graded. • Name: • SFU ID number: • Tutorial section number: General instructions 1. This is a closed-book exam: no books, notes, computer, cellphone, internet, or other aids. A scientific, non-graphing calculator is allowed. 2. If you use decimals in calculation, keep two decimal places. 3. Write clearly. Illegible answers will receive no credit. 4. Show your work! Partial credits are given. Answers without proper explanation/calculation will be penalized. 5. A request for regrade can be accepted only if the exam is written with a pen. 1. (10 points) Consider the following game: Player 1 and 2 simultaneously guess an integer between 1 and 3. If the numbers coincide, both win the amount they guess. If not, each loses the amount of his guess. (i) Write down the payoff matrix. (ii) Find the strategies that survive iterative deletion of strictly dominated strategies (ISD). For each strategy that you delete, write down the strategy that strictly dominates it. 1 (iii) Find the pure-strategy Nash equilibria. (iv) Find the symmetric, mixed-strategy Nash equilibrium. 2. (20 points) The market demand function for a homogeneous good is P (Q) = 9 − Q. There are two firms: firm 1 has a constant marginal cost of 1 for producing/selling each unit of the good, and firm 2 has a constant marginal cost of 5. (i) The two firms compete by simultaneously setting their prices (p1 and p2 ), and the firm with the lowest price captures the whole market (if the two firms set the same price, they split the market evenly). Assume the price that each firm sets must be in the increments of 0.01: for example, 1.98, 1.99, 2, 2.01, 2.02, ... Calculate a Nash equilibrium (p1 , p2 ) in this game, such that each pi is not a weakly dominated strategy. Explain why it is a Nash equilibrium. (ii) Now assume the two firms compete by simultaneously setting their quantities (q1 and q2 ), and the price of the good is determined by the market demand function given the total quantity. Calculate a Nash equilibrium (q1 , q2 ) in this game. 2