14.12 Game Theory-Midterm I
10/15/2003
Prof. Haluk Ergin
Instructions: This is an open book exam, you can use any written material. You
have 1 hour and 20 minutes. Each question is 35 points where the bonus question 3(c)
accounts for the extra 5 points. G
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Homework 3
Due on 10/31/2005
1. Two players rst simultaneously declare Yes or No. If any of the player declares No,
then each player gets 80. If both players declare Yes, then they play the following
game:
Invest
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Solution to Homework 3 Problem One a) This game has two subgames. One subgame is the game as a whole and the other is the subgame after both players say yes. In this last subgame we have 3 Nash equilibria (NE)
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Homework 4
Due on 11/7/2005
(You may return your homework until 11/9 in class,
but your homework will be graded before the midterm only if you submit it by 11/7.)
1. Consider the game in which the following stage
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Solution to Homework 4
1. Note that (A,L) is a Nash equilibrium of the stage game. Thus, for the
game where the stage game is repeated ve times, to play (A,L) in each
period is a strategy prole that is subgame-pe
14.12 Game Theory
Prof. Muhamet Yildiz
Fall 2005
Homework 5
Due on 11/23/2004 (in class)
Note: This is a very short homework. I expect that you will submit your
solutions on time. But since it is holiday, if you cannot turn in on time, you can
submit your
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Solution to Homework 5
1. Answer to Problem 1
(a) The game can be written formally as follows:
Actions space:A1 = cfw_X, Y, Z , A2 = cfw_L, R
Types space: T1 = cfw_t1 , T2 = cfw_ = 1, = 1
Beliefs: p( = 1|t1 ) = p
ART 101: ANCIENT AND MEDIEVAL ART
_
Film Worksheet #3:
Building the Great Cathedrals Nova documentary, PBS, 2010.
As you watch the film, take notes as you wish; but make sure to note the following information by filling in the
blanks.
(1) The film begins
ART 101: ANCIENT AND MEDIEVAL ART
_
Film Worksheet #1:
Cave of Forgotten Dreams, a film by Werner Herzog (2010)
As part of our study of Art Before History: The Origins of Image Making, you will view this
interesting film by Werner Herzog. Herzog narrates
ART 101: ANCIENT AND MEDIEVAL ART
_
Film Worksheet #2:
Part 3 of From Jesus to Christ: The First Christians, a
Frontline documentary, PBS, 1998.
Terms, People, Questions:
Josephus, Massada
Gospel
Aramaic, Greek
Synoptic
Messiah, parables, Messianic Secret
14.12 - Fall 05
Solutions for Problem Set #2
Question 1 (30)
By inspection, it can easily be seen that there is no pure strategy Nash Equilibrium of the game. Whenever
a cell is considered, it is always possible to nd a deviation by at least one of the pl
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Homework 2
Due on 10/7/2005
(The homeworks are accepted until 10/12, but you need to turn in your homework on due
date if you want to get your graded homework back on time.)
1. Find all the Nash equilibria of the
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Solution to Homework 1
Solution to Problem 1
a) (ten points) Lets rst nd appropriate payos for Alice. The information
stated in the question shows us that the payos will be of the form
Bob
AMH
Alice P a b b
Gba
c
14.12 Game Theory-Midterm I
10/15/2003
Prof. Haluk Ergin
Instructions: This is an open book exam, you can use any written material. You
have 1 hour and 20 minutes. Each question is 35 points where the bonus question 3(c)
accounts for the extra 5 points. G
14.12 Game Theory Fall 2004
Midterm 1 10/13/04 in class
(You have 80 minutes. Good Luck!) 1. Consider the following game: A B C a 3,0 0,3 0,x b 0,3 3,0 0,x c x,0 x,0 x,x a. (15pts) Compute two Nash equilibria for x = 1. b. (10pts) For each equilibrium in
14.12 Game Theory
Fall 2004
Answers for Midterm 1, Fall 2004
1. Consider the following game:
a
b
c
A
3, 0
0, 3
x, 0
B
0, 3
3, 0
x, 0
C
0, x
0, x
x, x
(a) The question does not ask to nd all Nash equilibria. One way is to nd all the pure-strategy Nash
equi
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Midterm 1
October 17th, 2005 (80 minutes)
Good Luck!
1. Below there are two pairs of games. For each pair check whether they represent the
same preference relation on the lotteries with strategy proles as their o
14.12 Game Theory
Fall 2005
Answers to Midterm 1, Fall 2005
Answer to Problem 1
a) Player 1 has the same payo function in both games, so player 1 trivially
has the same preference relation over lotteries with strategy proles as their
outcomes.
What about
Nice to know about CES functions
(preliminary)
Ferdinand Mittermaier
Department of Economics,
University of Munich, D-80799 Munich (Germany),
Phone: +49 89 2180 6752, E-mail: mittermaier@lrz.uni-muenchen.de
This set of derivations was prepared for the tut
14.126 (Game Theory) Final Examination
Instructions: This is an open-book exam you may consult written material
but you may not consult other humans. There are four questions, weighted equally.
You have 24 hours to complete the exam from the time you rst
14.126 (Game Theory) Final Examination
Instructions: This is an open-book exam you may consult written material
but you may not consult other humans. There are four questions, weighted equally.
You have 24 hours to complete the exam from the time you rst
14.126 Game Theory
Final Exam
You have 24 hours from the time you pick up the exam (i.e. you need to return
your solutions by the same time next day). You can use any existing written
source, but you cannot discuss the content of this exam with others. Qu
14.126 Game Theory
Final Exam
You have 24 hours from the time you pick up the exam (i.e. you need to return
your solutions by the same time next day). You can use any existing written
source, but you cannot discuss the content of this exam with others. Qu
14.12 Game Theory
Muhamet Yildiz
Fall 2005
Homework 1
Due on 9/28/2005 (in class)
1. Alice is visiting New York. She calls her friend Bob, who lives in New Haven, from
a pay phone, and they decide that Bob comes to New York and they meet at the
train stat
ART 101: ANCIENT AND MEDIEVAL ART
_
Pair & Share Discussion Reading Summary
Due: Th, March 10 in class
Length: half-page to a full page, single-spaced, 12-pt, Times Roman
For this class meeting, print out and read one of the following articles (A or B as