EMORY UNIVERSITY
DEPARTMENT OF ECONOMICS
ECONOMICS 487
Final Exam
Friday, April 30, 2010, 4:30 6:30 p.m.
Tilman Klumpp
Spring Semester, 2010
Instructions: Please read all questions carefully. This is a closed notes/closed books
exam. The exam has 40 point
13. Commitment
Commitment
Problem: How can a non-credible threat become a credible one? Create Strategic inflexibility: Eliminate options you have in the game (or make them very costly) This commits the player to certain actions which he would otherwise n
16. Finitely Repeated Games
Repeated Strategic Interaction
Often people play the same game over and over Possibility of different strategies arises Example: People can form relationships that benefit both in the long run
Supergame
t1 t2 s1 s2 s1 s2
t1 t
17. Infinitely Repeated Games
Model of an infinitely repeated game
Normal form stage game G Two players: i = 1,2 Action sets (=pure strategies): Si for player i Payoffs: ui (s1 , s2) for player Supergame Infinite rounds of play, t = 1, 2, 3, . Notation:
18. Bargaining and Negotiations
Rubinstein-Stahl Bargaining Model
Two players must split a pie of value 1 Proposal = x [0 , 1] = player 1s share (i.e. player 2 gets 1x) Alternating offers: Round t = 1: Player 1 makes proposal x(1) Player 2: Round t = 2: A
19. Bayesian Games
Imperfect Information vs. Incomplete Information
Games with imperfect information
There are information sets containing two or more nodes
Bayesian Games
(Games with incomplete information)
Some player knows exogenous payoff-relevant inf
20. Beliefs and Bayes Rule
Forming beliefs about unknown events
Example
Patient sees a doctor because she feels sick Initial examination: 50% chance of either condition A or B
Doctor runs an additional test to find out more Two possible test results, p
21. Signaling Games
What is signaling?
Players take costly actions to communicate information
People get an education even when it does not directly enhance productivity (it signals talent, intelligence, work ethic employers make job offers)
Businesses gi
22. Auctions and Competitive Bidding
Buying and selling
The Basic Selling Problem Seller has a single good for which she has a zero value One or more buyers have privately known valuations (=willingness to pay) for the good If the seller knows the buyers
Comparison of auction formats
Which format should the seller choose? Goal: Maximize revenue (obtain as high a price as possible)
Trade-off the seller faces:
First-price format: Price equals highest bid . . but highest bid is below highest value (bid-shadi
EMORY UNIVERSITY DEPARTMENT OF ECONOMICS ECONOMICS 487, Spring 2010 Chapter Summaries (Units IIIIV
Below is a brief summary of the topics we have covered in the second half of Economics 490S, containing the most important points only. For details, applica
Equilibrium Existence
Theorem (Nash 1950):
Every finite normal form game possesses an equilibrium
(possibly in mixed strategies).
Finite game = game with finitely many players, strategies.
Can you come up with an infinite game which does not
possess an eq
5. Nash Equilibrium in
Two-Player Games
No dominance relations in most games
Coordination Game
Battle of the Sexes
Pl. 2
Pl. 2
A
A
1,1
B
W
W
0,0
Pl. 1
O
6,2
1,1
O
0,0
2,6
Pl. 1
B
0,0
1,1
Chicken
Pl. 2
Str
Swe
Str
0,0
6,4
Swe
4,6
5,5
Pl. 1
Idea for a solut
EMORY UNIVERSITY
DEPARTMENT OF ECONOMICS
ECONOMICS 487, Spring 2011
Take Home Test #1
(Due: February 10, 2011, 11:30 am)
Instructions. There are seven questions, totaling 50 points. Please include all graphs,
calculations, and/or verbal reasoning you use
EMORY UNIVERSITY
DEPARTMENT OF ECONOMICS
ECONOMICS 487, Spring 2011
Take Home Test #2
(Due: March 17, 2011, 11:30 am)
Instructions. There are six questions, totaling 50 points. Please include all graphs,
calculations, and/or verbal reasoning you use in ar
Player 1
U
M
EMORY UNIVERSITY D DEPARTMENT OF ECONOMICS
Player 2 ECONOMICS 487, Spring 2010
L 2,0
C 6,2
LAnswers forLTake C C Home Test #1 3,4 3,2 7,6 4,8
Question 2. One normal form representation (there are several) of the game tree is the following:
Pl
EMORY UNIVERSITY DEPARTMENT OF ECONOMICS ECONOMICS 490S, Spring 2007 Answers for Chapter 16
Question 1. Battle of the Sexes is a 2 2-payo matrix. That means it has 4 outcomes; if it is repeated twice it has 16 outcomes. So if it was repeated three times,
EMORY UNIVERSITY DEPARTMENT OF ECONOMICS ECONOMICS 490S, Fall 2006 Answers for Chapter 18
Question 1. We did this in class; please refer to your notes or to the slides for Chapter 17. Question 2. If player 1 randomizes between W and O with equal probabili
EMORY UNIVERSITY DEPARTMENT OF ECONOMICS ECONOMICS 490S, Fall 2006 Answers for Chapter 19
Question 1. With the new prior probabilities, the Bayesian posterior likelihoods are computed as follows: In information set + we have P r[A|+] = 0.3 0.9 0.6585, 0.3
EMORY UNIVERSITY DEPARTMENT OF ECONOMICS ECONOMICS 490S, Fall 2006 Answers for Chapter 21
Question 1. Dene z (1) = maxcfw_z1 , z2 , z3 [0, 1], the highest of the three valuations (i.e. the rst-order statistic of the zi .) With three bidders, each bidders
EMORY UNIVERSITY DEPARTMENT OF ECONOMICS ECONOMICS 490S Final Exam Wednesday, May 6, 2009, 4:30 6:30 p.m.
Tilman Klumpp
Spring Semester, 2009
Instructions: Please read all questions carefully. This is a closed notes/closed books exam. The exam has 40 poin
4. Dominance solvable games
Famous example: Prisoners Dilemma
Prisoner 2
Silent
Silent
Prisoner 1
Confess
1 , 1
10 , 0
Confess
0 , 10
8 , 8
In general, any game
of this form is called a
prisoners dilemma:
Player 2
Cooperate
Cheat
Cooperate
a,a
d,c
Cheat
c
Game Theory
Professor S. Mialon
Handout 7-1: Ch 10 Bayesian Nash Equilibrium
<Swing Voters Curse>
Suppose that whether candidate 1 or 2 is elected depends on the vote of two citizens, Sue and
Tim. A candidate wins if he/she obtains more votes than the oth