S2010_Exam1_solutions

S2010_Exam1_solutions - Econ 171 (Grossman) Spring 2010...

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Unformatted text preview: Econ 171 (Grossman) Spring 2010 Exam 1 April 20 You have 75 minutes to take this exam. Please answer all 6 questions, each of which is worth 5 points. Point subtotals are indicated. Show your work to obtain full credit. Part 1 4 questions, 20 points (5 each) For each game in this part, please find a) The set of profiles of pure-strategies that are rationalizable. ( 3 points in question 1, 2 points otherwise ) b) All Nash equilibria ( 2 points in question 1, 3 points otherwise ) 1. Only for this game , for each strategy that you eliminate, name the strategy that dom- inates it. X Y Z A 2 , 1 2 , 5 2 , 7 B , 1 4 , 6 6 , C 7 , 3 5 , 1 , 1 Answer: ( C,X ) is the unique rationalizable strategy profile and the unique NE. Iterated elimination steps: A is eliminated because it is dominated by (0 , 1 / 2 , 1 / 2), that is a 50-50 mix between B and C Z is eliminated because it is dominated by (1 / 2 , 1 / 2 , 0), that is a 50-50 mix be- tween X and Y B is eliminated because it is dominated by C Y is eliminated because it is dominated by X Only C and X remain 1 X Y Z A 4 , 2 5 , 2 1 , 1 B 1 , 3 4 , , 2 C 3 , 1 2 , 3 1 , 2 2. Answer: ( A,X ) and ( A,Y ) both rationalizable and NE. The full set of NE are ( A, ( p, 1- p, 0)) for any p [0 , 1]. You could also write ((1 , , 0) , ( p, 1- p, 0)). 2 X Y Z A 4 , 1 , 1 2 , 1 B 2 , 1 6 , 3 , C 3 , 2 2 , 3 , 4 3. Answer: ( B,Y ), ( B,Z ), ( C,Y ), ( C,Z ) all rationalizable. PSNE: ( B,Y ) and ( C,Z )....
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S2010_Exam1_solutions - Econ 171 (Grossman) Spring 2010...

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