M361K (56225) Midterm 1 practice problems
1. Let A and B be sets. Show that
(A B ) \ (A B ) = (A \ B ) (B \ A).
2. Show that the set
Nk
S=
kN
is countable, where
Nk = N N .
k times
3. Show that the set of all functions N N is not nite or countable.
4. Sho
M361K Lecture Notes
Samuel Isaacson
September 17, 2012
Abstract
These are the typed lecture notes for M361K, unique number 56225, from Autumn
2012. This course is a rigorous introduction to real analysis. Topics include the denition and topology of R, con
M361K (56225) Problem Set 1
1. Suppose I = . Let cfw_Ai iI be a nonempty family of subsets of a set B . Prove De
Morgans Laws, i.e.,
B\
(B \ Ai )
B\
(1)
(B \ Ai )
Ai =
i I
(2)
i I
Ai =
i I
i I
2. Let f : X Y be a map of sets.
(a) Suppose A, B Y . Show tha
Solutions to
Problem Set No. 5
1. Represent the game of Marienbad with a starting configuration of 3 matches
in each pile in extensive form.
Marienbad: There are two piles of matches and two players. The game starts
with player 1 and thereafter the player
Solutions to
Problem Set No. 6
1. The Military Draft.
All register! When called, as long as no one earlier failed to register,
they will register.
2. Entry Deterrence.
(a), (b) Entrant In; Incumbent Accommodate.
(c) Entrant Out; Incumbent Retaliate.
EU(Ac
Econ 354K Game Theory
Solutions to
Problem Set No. 2
1. Draw the firms decision tree.
Manila
ship
2
truck
4
New York
train
3
New York
($75)
ship
truck
($79)
train
ship
($95)
train
New Orleans
ship
truck
truck
($77)
New Orleans
5
train
New Orleans
($82)
sh
Prof. Stahl
354K - GAME THEORY
Sample Exam 1
* Put your 4-digit code ONLY at the top of every answer sheet.
* Start your answers for each question at the top of a NEW page.
1. (20%)
a)
b)
c)
d)
Briefly define the following terms:
event;
information set;
p
Prof. Stahl
Eco 354K - Problem Set 6
1. The Military Draft. During the Vietnam War, the US government wanted to motivate
teenagers to register for the military draft. The problem faced by the government was that it
would be impossible to punish everyone i
F '12
Prof. Stahl
Eco 354K - Problem Set 5
Due Tues, Oct 2
1. Dutta, 11.4
2. Dutta, 11.5
3. (a) Solve the following game by backward induction. [There are two such solutions.]
1.1
L
M
2.1
2.2
u
3.2
l' c'
02
03
03
r'
1
0
2
R
d
u' m'
1.2
L' M' R'
1
4
2
3.1
F'12
Prof. Stahl
354K Game Theory
Problem Set No. 4 - due 09/20
1) Ronald is indifferent between $100 for sure and a 50% chance of $1000 or
nothing. He is also indifferent between $10 for sure and a 10% chance of $1000
or nothing. (a) Assuming Ronald's pr
F'12
Prof. Stahl
354K Game Theory
Problem Set No. 3; due 09/13
1) An executive at a publishing house has just received two stock options as a bonus.
Each of these options gives the executive the right (but not the obligation) to purchase
one share of the