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S2010_Exam2 - NAME Econ 171(Grossman Spring 2010 Exam 2 May...

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NAME: Econ 171 (Grossman) — Spring 2010 Exam 2 May 13 You have 75 minutes to take this exam. Please answer all 4 questions, each of which is worth 15 points. Point subtotals are indicated. Show your work to obtain full credit. 1. Consider the extensive-form game shown in Figure 1. R L 1 r 1 2 , 1 l 1 1 , 2 2 r 2 l 2 0 , 3 2 r 1 , 4 l 2 , 2 1 Figure 1: The game from question 1. (a) [5] List the strategies for each player. (b) [5] Find the Nash Equlibria. (c) [5] Apply backwards induction and state the resulting SPNE. 1
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B A 5 , 5 1 D C 2 F 4 , 0 E 6 , 6 F 4 , 4 E 0 , 4 1 Figure 2: The game from question 2. 2. Consider the game shown in Figure 2. (a) [5] Find all the pure-strategy Nash equilibria of this game. (b) [5] Which of these are subgame perfect? (c) [5] Challenge question : There is a concept called forward induction that can be used to argue that one of the SPNE is unreasonable. We haven’t studied it in class, but the name kind of gives you a hint as to how to apply it. Look at the SPNE and try to come up with an argument for why one of them should be elim- inated. Briefly explain your argument.
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