S2010_Exam2_solutions

# S2010_Exam2_solutions - NAME Econ 171(Grossman — Spring...

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Unformatted text preview: NAME: Econ 171 (Grossman) — Spring 2010 Exam 2 — Solutions 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 , 3 2 r 1 , 4 l 2 , 2 1 Figure 1: The game from question 1. (a) [5] List the strategies for each player. Answer : S 1 = { Ll, Lr, Rl, Rr } and S 2 = { l 1 l 2 , l 1 r 2 , r 1 l 2 , r 1 r 2 } (b) [5] Find the Nash Equlibria. Answer : ( Ll, l 1 l 2 ) and ( Lr, l 1 l 2 ) (c) [5] Apply backwards induction and state the resulting SPNE. Answer : 1 B A 5 , 5 1 D C 2 F 4 , E 6 , 6 F 4 , 4 E , 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. Answer : ( BE, C ), ( AE, D ), and ( AF, D ) (b) [5] Which of these are subgame perfect? Answer : ( BE, C ) and ( AF, D ) (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 inused to argue that one of the SPNE is unreasonable....
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## This note was uploaded on 12/26/2011 for the course ECON 171 taught by Professor Charness,g during the Fall '08 term at UCSB.

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S2010_Exam2_solutions - NAME Econ 171(Grossman — Spring...

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