S2010_final_sols

# S2010_final_sols - Econ 171 Spring 2010 Final Exam June 8 You have three hours to take this exam Please answer all 5 questions for a maximum of 100

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Econ 171 Spring 2010 Final Exam June 8 You have three hours to take this exam. Please answer all 5 questions, for a maximum of 100 points. Point totals and subtotals are indicated in brackets. To obtain credit, you must provide arguments or work to support your answer. 1. [10] Find all Nash equilibria of the following game. X Y Z A 2 ,- 1 4 , 2 2 , B 3 , 3 , 1 , 1 C 1 , 2 2 , 8 5 , 1 Solution : There are three equilibria. ( B,X ) and ( A,Y ) are PSNE and (( 4 5 , 1 5 , 0) , ( 1 2 , 1 2 , 0)) is a mixed-strategy Nash equilibrium. 1 2. [20] Consider the extensive-form game represented below. C A 5 , 2 B 1 Y 6 , 2 X 2 , 6 Y 2 , 6 X 6 , 2 2 (a) [5] Which solution concept is the appropriate one to apply to this game? Find the set of equilibria using that concept. Solution : Perfect-Bayesian Equilibrium is the appropriate solution concept (be- cause it discards equilibria that are not sequentially rational). The only kind of PBE is of the following form: ( A, ( p, 1- p )), where p = Pr( X ) ∈ [ 1 4 , 3 4 ], and player 2’s beliefs are given by μ 2 ( B ) = μ 2 ( C ) = 1 2 . (b) [5] Suppose that we delete the information set between player 2’s two decision nodes. (Plugging the values ( a,b,c ) = (5 , 6 , 2) into the figure below shows the extensive form of this game.) In other words, suppose that 2 can actually observe whether 1 chose B or C . What solution concept should we apply now? Find the unique equilibrium under that concept. Solution : Now we should apply SPNE, which yields ( A,XY ). (c) [5] Now let ( a,b,c ) = (3 , 1 , 3). Find all PSNE of this game. Solution : The PSNE are ( A,XX ), ( A,XY ), and ( C,XY ). (d) [5] Which of these are subgame-perfect? Solution : ( A,XY ) and ( C,XY ) are subgame-perfect. C A a, 2 B 1 Y 6 , 2 X 2 , 6 2 Y c, 6 X b, 2 2 2 3. [10] Suppose two players play one of the two normal-form games shown below. Player 1 knows which game is being played, but player 2 thinks that it is Game (a) with...
View Full Document

## 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.

### Page1 / 6

S2010_final_sols - Econ 171 Spring 2010 Final Exam June 8 You have three hours to take this exam Please answer all 5 questions for a maximum of 100

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online