n
ECON 212-Game Theory
Spring 2012
Problem set 6, due Thursday, March 22
Question 1 )
Watson, chapter 15, question 2 and 4
Question 2 )
Watson, chapter 16, questions 2, 7, and 8
Question 3 )Nobel Laureate Thomas Schelling once proposed a solution to the p
n
ECON 212-Game Theory
Spring 2012
Problem set 9, due Tuesday April 24.
Question 1 )
Watson, chapter 26, question 2
Question 2 )
Watson, chapter 27, questions 2 and 6
Question 3 ) (Information might be harmful!)
Consider the following two-player game: Pla
Economics 101
Problem Set 1 Answer Key
Due September 18, 2012
Question 1
For each of the following functions f (x1 , x2 ), (1) Find the rst order condition for a maximum;
(2) Solve for x , x ; (3) Find the value of f (x , x ) i.e. the value of the functio
Economics 212
Fall 2012
Steven A. Matthews
University of Pennsylvania
Suggested Solutions to Exam 2
Closed books, notes, and all electronics. 1 1 hours. 100 points.
4
Indicate your reasoning. Read all questions before answering any.
1. (20 pts) Find all N
ECON 212-Game Theory
Spring 2012
Problem set 6, answer key
1. Problem 2 on page 176 (chapter 15)
1. This game has 3 subgames: (1) the subgame following the move W by player 1;
(2) the subgame following the move Z by player 1; and (3) the game itself. The
ECON 212-Game Theory
Spring 2011
Problem set 7, answer key
1. Problem 1 on page 212 (chapter 18)
1. dJ = 0; dR = 0; vJ (x) = 10; 000
1
1
f0; 1g; J = 2 ; R = 2
6; 000x, vR (x) = 40; 000 + 4; 000x, x 2
The bargaining set is graphed below:
The joint value wh
ECON 212- Game Theory (Spring 2013)
Midterm exam #1
Important: [1] This is a closed-book exam. No books, notes, calculators,
computers, phones. [2] You have 80 minutes to complete the exam. [3]
Answer all questions. [4] For full credit, you must show your
ECON 212-Game Theory
Spring 2012
Problem set 4, answer key
1. Problem 3 on page 129 (chapter 11)
1. The normal-form game we are analyzing is
X Y
L
N
L
5; 5 x 15; 0
N
0; 15
10; 10
This game has two Nash equilibria: (L; N ) and (N; L).
The best response to
Economics 212
Problem Set 5 Solutions
December 2, 2012
Steven Matthews
1. Problem 1 on chapter 18
(a) dJ = 0, dR = 0, vJ (x) = 10, 000 6, 000x, vR (x) = 40, 000 + 4, 000x, x cfw_0, 1, J =
R = 1
2
The bargaining set is graphed below:
The joint value when x
Economics 212
Fall 2012
Steven A. Matthews
University of Pennsylvania
Solutions to Exam 1
1
Closed books, notes, and calculators. 1 4 hours. 100 points.
Indicate your reasoning. Read all questions before answering any.
1. (30 pts) Dorothy (D) and John (J)
Economics 101
Problem Set 2 Answer Key
Due September 25, 2012
Please indicate your recitation time/number and recitation instructor on your answer.
1
Denitions and Reading Comprehension
For each of the following, write a short denition, in words (one sent
1
ECON 212- Game Theory (Spring 2011)
Midterm exam #1
Important: [1] This is a closed-book exam. No books, notes, calculators, laptop
computers, cell phones. [2] You have 80 minutes to complete the exam. [3] Answer
all questions. [4] For full credit, you
ECON 212 Game Theory
Spring Term 2012
PROBLEM SET 4
Due in class on Thursday February 23
Question 1
Watson, chapter 11, questions 3, 4, and 8
Question 2
An attack group commander has a single plane which can strike one of three possible targets.
The defen
ECON 212-Game Theory
Spring 2012
Problem set 5, answer key
1. Problem 2 on page 153 (chapter 13)
The partnership game we are analyzing is:
1 2
I
N
I
4,4 -4,9
N
2,-4 0,0
1. If the court imposes expectation damages, the induced game is represented by the
fo
Economics 101
Problem Set 6
Due November 21, 2012 at noon
Please indicate your recitation time/number and recitation instructor on your answer.
1
Denitions and Reading Comprehension
For each of the following, write a short denition, in words (one sentence
ECON 212-Game Theory
Repeated Games (W22, 23)
Spring 2011
Motivating Intuition
I
A repeated game is a special kind of an extensive form game
where the same one-shot "stage" game is played over and
over again
I
In a one-shot game, a good outcome may not be
ECON 212-Game Theory
Bayesian Games
Spring 2012
Games of Incomplete Information
I
Example: Gunght in the wild west
I
Under full information:
I
I
I
Unique equilibrium in matrix (a) is (Draw, Draw)
Unique equilibrium in matrix (b) is (Wait, Wait)
Incomplete
1
ECON 212- Game Theory (Spring 2011)
Midterm exam #1
Important: [1] This is a closed-book exam. No books, notes, calculators, laptop
computers, cell phones. [2] You have 80 minutes to complete the exam. [3] Answer
all questions. [4] For full credit, you
Economics 212 Honors
Spring 2009
Steven A. Matthews
University of Pennsylvania
Solutions to Midterm 1
1
Closed books, notes, and calculators. 1 4 hours.
Indicate your reasoning.
100 points total.
1. (15 pts) Consider the following game.
X
Y
Z
A
0; 2
3; 1
ECON 212- Game Theory (Spring 2012)
Final exam
Important: [1] This is a closed-book exam. No books, notes, calculators, laptop
computers, cell phones. [2] You have 120 minutes to complete the exam. [3] Answer
all questions. [4] For full credit, you must s
ECON 212-Game Theory
Industrial Organization/ Stackelberg Game
Spring 2012
Cournot Duopoly Game (again)
I
Two rms, 1 and 2. Ci (qi ) = 0.
P ( q1 + q2 ) = P ( Q ) = 1 Q
I
ui ( q1 , q2 ) = ( 1
I
The best reply function of rm 1: Maximizes u1 (q1 , q2 ) with
ECON 212-Game Theory
Standard Bargaining Solution & Holdup
Spring 2012
The Standard Bargaining Solution (Nash cooperative
s
bargaining solution)
I
This is a cooperative game theory concept for situations with
transferable utility. Here are the primitives
C H A P T E R O N E
A Survey of Auction Theory*
This chapter provides an elementary, non-technical survey of auction theory, by
introducing and describing some of the critical papers in the subject. (The most
important of these are reproduced in a compani
ECON 212-Game Theory
STRATEGIC LESSONS FOR THE REST OF YOUR LIVES
Spring 2012
I
Games involve interaction with other purposive players.
(Nash) equilibrium concept recognizes this
I
Most games have a mixture of conict and common interest.
Balancing the two
ECON 212 Game Theory
Spring Term 2012
PROBLEM SET 2
Due in class on Thursday February 2
Question 1
Watson, chapter 4, questions 1 and 2
Question 2
Watson, chapter 6, questions 1, 2, and 7
Question 3
Watson, chapter 6, question 4 (the game of RockPaperScis
ECON 212-Game Theory
Spring 2012
Problem set 2, answer key
Question 1)
Watson, chapter 4, question 1: We are analyzing the following normal form game:
1 2 L
U
10, 0
M
2, 10
D
3, 3
1.
C
0, 10
10, 2
4, 6
R
3, 3
6, 4
6, 6
1. u1 (U; C) = 0
2. u2 (M; R) = 4
3.
ECON 212 Game Theory
Spring Term 2012
PROBLEM SET 5
Due in class on Thursday March 1
Question 1
Watson, chapter 13, questions 2, 3, and 9
Question 2
Each of three players is deciding between the pure strategies go and stop. The payoff to go is
120/m where
ECON 212 Game Theory
Spring Term 2012
PROBLEM SET 1
Due in class on Thursday January 26
Question 1
Watson, chapter 2, questions 3 and 5
Question 2
Watson, chapter 3, questions 2, 3 [parts (a), (c), (e), and (f)], and 4
Question 3
Consider a setting in whi
ECON 212-Game Theory
Spring 2012
Problem set 8, answer key
1. Problem 1 on page 271 (chapter 22)
We are analyzing a two-period repetition of the following stage game:
1 2 L
M R
U
8,8 0,9 0,0
C
9,0 0,0 3,1
D
0,0 1,3 3,3
Note that this stage game has 3 Nash
Economics 212
Fall 2013
Steven A. Matthews
University of Pennsylvania
Solutions to Midterm 1
Closed books, notes, and calculators. 1 41 hours. 100 points.
Indicate your reasoning. Read all questions before answering any.
1. (15 pts) Consider a game played
Econ 212 Game Theory
Lecture Slides 12
Bargaining Games
(W19)
Steven A. Matthews (UPenn)
University of Pennsylvania
March 19, 2017
Steven A. Matthews ()
Bargaining Games
March 19, 2017
1 / 25
The Bargaining Problem
Refers to situations in which there are
Economics 212
Fall 2013
Steven A. Matthews
University of Pennsylvania
Midterm 1
Closed books, notes, and calculators. 1 41 hours. 100 points.
Indicate your reasoning. Read all questions before answering any.
1. (15 pts) Consider a game played by Joan and
Econ 212 - Solutions to PS3
Joao Vitor Granja de Almeida
March 16, 2017
Chapter 11, Question 4
Lets start with the two by two game. Suppose (1 , 2 ) = (p, 1p), (q, 1
q) is a mixed strategy equilibrium. Note that u1 (A, q) = 2q and u1 (B, q) =
q + 3(1 q).
Econ 212 - Solutions to PS2
Joao Vitor Granja de Almeida
February 9, 2017
Chapter 7, Question 1
(a)
Start with player 1. Note that if player 2 plays X, D is a best reply;
if player 2 plays Y , U is a best reply. It remains to check if M is dominated
or no