This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 purestrategies 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 5050 mix between B and C • Z is eliminated because it is dominated by (1 / 2 , 1 / 2 , 0), that is a 5050 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 )....
View
Full Document
 Fall '08
 Charness,G
 Petter, MARIT, Matching Pennies game, unique rationalizable strategy

Click to edit the document details