Revised 05/08/2019 11:000 PM
MTH 460/560--Theory of Games--Homework Assignments
Homework: due Mondays in lecture
Quiz (460 only): Fridays in
recitation
Exams:
- Exam I: Friday, March 1 completed
- Exam II: Friday, March 29 completed
- Exam III: Friday, April 26
- Final Exam: Wednesday, May 15,
2019, 8:00 - 11:00, in Math 250
Office Hours:
Course Material--UBlearns > Course
Documents
Textbook:
- Playing for Real: A Text on Game Theory by Ken Binmore
- "Solution Manual": Google: solution manual playing for real
- this is supposed to be the solutions you would find at the back of
the book
- this manual is not always correct, or complete, or useful
- sometimes misses the point of a problem
- merely copying from the solution manual will get a 0 on the homework
Problems in brackets [ ] should be looked at, the rest should be done and
turned in.
Week of May 6
- Quiz for 460: Quiz on Friday, May 10 in recitation
- Assignment (these are possible exam questions, not to be
turned in):
- p 207: 1, 9, 18
- If you want to try a really hard problem: p 207: 3
Final Exam
- When: Wednesday, May 15, 8:00 AM - 11:00 AM
- Where: Math 250
- Covers: 1.1 - 3.7.1, 4.1 - 4.8.1, 5.1 - 5.2.2, 5.4,
6.1 - 6.4
- including
homework assignments and the corresponding material on the
lecture slides/notes
- includes
the method of section 5.2.2
- include Gale's roulette (Chapter 3: 31 and 33)
- includes the Basic Principle of Mixed Strategies in Lecture notes
for 05/08/2019
- Format: 1 - 3 definitions or
statements of result, 6 - 10 problems
- Calculators: Only
non-programmable, non-graphing, non-alphanumeric are allowed on exams
Coming Attractions (tentative list of upcoming assignments):
Assignment 1--week of January 28--School was cancelled on Wednesday,
January 30. No recitation, no quiz, no homework
- Recitation: will meet on Friday,
February 1 at 8:00 AM in Math 250
- Read: Chapter 1, through 1.7
- Quiz for 460: Friday, February 1 in recitation
- Turn in Problem Set 1: (from the text book), due 02/04/19 in
class
Week of February 4
- Recitation: Friday, February 8 at 8:00 AM in Math 250
- Read: Chapter 1
- Quiz for 460: Friday, February 8 in recitation
- Topics: 1.1 - 1.8, including
- the mathematical definition of Nash equilibrium (see presentation
in UBLearns>Course Documents>Miscellaneous)
- bimatrices, how to find Nash equilibrium, strong dominance,
prisoner's dilemma/delight
- Format: one definition or statement, one problem
- Turn in Problem Set 1: (from the text book), due 02/11/19 in
class
- p 33: 2, 3, 5 - 7, 9, 10
- p 33: 14
Week of February 11
- Read: Chapter 2.3.2 - 2.8.2
- Quiz for 460: Friday, February 15 in recitation
- Topics: 1.9 - 1.10, 2.3.2 - 2.4
- Turn in Problem Set 2: (from the text book), due 02/18/19 in
class
- p 33: 16, 17, 18, [19], 20
- Note: in Problem 16 the milk production is given by e^{1 - 1/(Aa)
} , so the A and "a" are both in the denominator
- Note: Problem 18 is a 100-person game, not a 2 player game
- Don't try to draw an outcome table, just explain why all
100 players voting/not voting is not a Nash equilibrium
- "Exercise
I"
- p 70: 1, 5 (draw to a depth of 4),
- Note: For problem 1, a saddle point is a strategy
pair that is worst in the row for P1 and best in the column for P1
- Note: Fig. 2.18 for
Problem 1 has a typo; second node c should be an e.
Week of February 18
- Read: Chapter 2.8 - 3.6
- Quiz for 460: Friday, February 22 in recitation
- Turn in Problem Set 3: (from the text book), due 02/25/19 in
class
- p 70: 8 (explain your reasoning)
- p 70: 2, 3
- Exercise
II
- Exam I: Friday, March 1
Week of February 25
- Read: Chapter 3.1 - 3.6
- Quiz for 460: No quiz on Friday, March 1 in
recitation
- Turn in Problem Set 4: (from the text book), due 03/04/19 in
class
- p 70: 6 (figure 2.18, p 71), 10 (3 x 3 only;
explain), 12 (do Beck's Hex 3 x 3 only, but explain "playing anywhere"
in general)
- Note: Problem 12: "playing anywhere" means that
you can place the marker arbitrarily
- p 70: 13, [16, 17]
- Note: you may use the
version of the game from problem 13 in problems 10 and 12, if you
wish
Week of March 4
- Read: Chapter 3.1 - 3.6
- Quiz for 460: Quiz on Friday, March 8 in recitation
- Turn in Problem Set 5: (from the text book), due 03/11/19 in
class
- p 70: 18
- p 70: 20, 21, 26
- Note: for a definition of
Tactical/Strategic voting (Problem 26) see first lines of wikipedia
article
Week of March 11
- Read: Chapter 3.1 - 3.6
- Quiz for 460: Quiz on Friday, March 15 in recitation
- Topics: 2.9, 2.2, 2.3
- Includes Reference Example IV (UBLearns lecture notes for
2019/03/13)
- Turn in Problem Set 6: (from the text book), due 03/25/19 in
class
- p 70: 22 - 24
- Note: the diagram for #23
is missing a 't' on the left edge coming from the root
- p 104: [1], 5
Week of March 25
- Read: Chapter 3.1 - 3.6
- Quiz for 460: no quiz on Friday, March 29 in
recitation
- Turn in Problem Set 7: (from the text book), due 04/01/19 in
class
- p 104: 9 -13
- Notes for Problem 9, p 104:
- formula at bottom of page 105 should have x raised to
power n + 1, not n .
- the frequency
of girls in a family is the ratio of girls to total children. Some
families will have frequency 0, some will have close to 1.
Figure out the expected frequency.
- Note for Problem 11, p 104:
should be figure 3.5
- p 104: 8 (#8 is later material than 9-13)
Week of April 1
- Read: Chapter 3.7, 4.1 - 4.3
- Quiz for 460: Quiz on Friday, April 5 in recitation
- Topics: Win/lose lotteries, Monty Hall, waiting games
- Turn in Problem Set 8: (from the text book), due 04/08/19 in
class
Week of April 8
- Read: Chapter 4.3 - 4.6
- Quiz for 460: Quiz on Friday, April 12 in recitation
- Turn in Problem Set 9: (from the text book), due 04/15/19 in
class
- {{p 104: 21, 23, 24 (skipping Duel; these three
problems will not be assigned)}}
- p 136: 3-7, 9-10 (don't read too much into Problem
10; it's not as complicated as Section 4.3.1)
- Typos in Section 4.3.1: 6th
line from bottom of p 114--should be "Pandora can buy gin at $10 a
bottle, vodka at $15" (book has them switched)
Week of April 15
- Read: Chapter 4.3 - 4.6
- Quiz for 460: Quiz on Friday, April 19 in recitation
- Topics: 4.5.2
- definition of VNM utility function
- Postulates of Rational Behavior
- Turn in Problem Set 10: (from the text book), due Wednesday,
04/24/19 in class
- p 136: 11, 12, 14, 15, 22
- We'll talk about risk aversion on Friday: 4.5.3
- Exam III: Friday, April 26
Week of April 22
- Read: Chapter 4.7 - 4.8
- Quiz for 460: No quiz on Friday, April 26 in
recitation
- Turn in Problem Set 11: (from the text book), due Wednesday,
05/01/19 in class
- p 136: 17, 23
- Note: in problem 17, a and b are the players'
utilities for disgrace (see beginning of Section 4.7)
Week of April 28
- Read: Chapter 4.7 - 4.8
- Quiz for 460: Quiz on Friday, May 3 in recitation
- Topics: Russian Roulette including 5.2.2
- order on vectors: u < v , u << v ,.u ≤ v
- Turn in Problem Set 12: (from the text book), due Monday,
05/06/19 in class
- p 168: 3, 8, 9, 10
- Note for #10: Use figure 5.15 at bottom of p
169.
- Find 2 payoff tables:chance moves up, chance moves down. Combine
to get overall payoff table
Exam I
- When: Friday, March 1 at 8:30 AM in Math 250 NOTE
CHANGE IN TIME
- Covers: Through 2.4, 2.6
- including
homework assignments and the corresponding material on the
lecture slides/notes
- includes mathematical definition
of Nash equilibrium in n-player game
- Format: 1 or 2 definitions or
statements of result, 4 or 5 problems or "show that"s
- Calculators: Only
non-programmable, non-graphing, non-alphanumeric are allowed on exams
Exam II
- When: Friday, March 29 at 9:00 AM in Math 250
- Covers: Chapter 2, 3.1
- including
homework assignments and the corresponding material on the
lecture slides/notes
- Includes Reference Example IV (UBLearns lecture notes for
2019/03/13)
- Format: 1 or 2 definitions or
statements of result, 3 to 5 problems or "show that"s
- Calculators: Only
non-programmable, non-graphing, non-alphanumeric are allowed on exams
Exam III
- When: Friday, April 26 at 8:30 AM in Math 250 NOTE
CHANGE IN TIME
- Covers: 3.2 - 3.7.1, 4.1 - 4.8, but skip 4.4
and 4.7
- including
homework assignments and the corresponding material on the
lecture slides/notes
- Format: 1 or 2 definitions or statements of result, 3
to 5 problems or "show that"s
- Calculators: Only
non-programmable, non-graphing, non-alphanumeric are allowed on exams