Revised 05/08/2021 10:25 PM
MTH 460/560--Theory of Games--Homework Assignments
Homework: due Mondays in
Gradescope by Midnight
Quiz (460 only): Fridays in
recitation
Exams:
- Exam I: Wednesday, March 17, 9:10 - 10:00 AM
remote, two-device proctored completed
- Exam II: Wednesday, April 21, 9:10 - 10:00 AM
remote, two-device proctored completed
- Final Exam: Wednesday, May 12,
2021, 8:00 - 11:00 AM remote, two-device proctored
Office Hours: TR 5:00 - 5:50
via Zoom and by appointment
Course Material--UBlearns > Course
Documents
- LaTex template
- Convex Hull
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 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
and is a violation of the Academic Integrity Policy
Problems in brackets [ ] should be looked at, the rest should be done and
turned in.
Assignment 14--week of May 3
- Quiz for 460: No quiz on Friday, May 7 in recitation
- Turn in Problem Set 13: (from the text book), due 05/10/21 in
gradescope by 11:59 PM
- p 207: 2, 3, 20
- 2 is a hard problem
- 3 is an even harder problem
Final Exam
- When: Wednesday, May 12, 08:00 - 11:00 AM, zoom
proctored, details will be forthcoming
- Covers: 1.1 - 2.9.3, 3.1 - 3.7.1,
4.1 - 4.6, 4.8.1, 5.1, 5.2, 6.2, 6.3, 6.4.5
- including the
corresponding material on the lecture slides/notes
- including the homework,
which has interesting examples not covered in the text
- Format: 8 to 10 problems or
"show that"s
- UB ID card must be shown to gain admittance to exam
- Calculators: Only
non-programmable, non-graphing, non-alphanumeric are allowed on exams
- Notes: None
- Internet resources: None are allowed--not to solve
problems, to do problems, or to check solutions
- Collaboration: None. This is to be your own,
individual work
- Exam time: available at 08:00 AM on Wednesday, May 12
- Due in Gradescope: 11:10 AM on Wednesday, May 12
- Submit in black or blue ink, handwritten only
- Be sure to match each
problem in Gradescope to the page in your work where the problem can
be found
- E.g., if problem 3 is on page 4, indicate this to Gradescope
Coming Attractions (tentative list of upcoming assignments):
- Final Exam on Wednesday, May 12, 2021, 8:00 - 11:00
AM remote, two-device proctored
Assignment 1--week of February 1
- Read: Chapter 1, through 1.7
- Recitation: Friday, February 5 at 11:30 AM remote
- Quiz for 460: Friday, February 5 in recitation
- Topics 1.1 - 1.3 Note change (had been 1.4)
- Available in UBLearns>Course Documents>Quizzes at 12:10 PM on
Friday, February 5
- Written in dark ink
- PDF of your solution is due in Gradescope by 12:25 PM on Friday,
February 5
- Turn in Problem Set 1: (from the text book), due 02/08/21 in
gradescope by 11:59 PM
- p 33: 1, 3, 7, 9
- homework should be typed, preferably in LaTeX. 560 Students must use
LaTeX
- LaTeX resources: UBLearns>Course Documents
Assignment 2--week of February 8
- Read: Chapter 1.7 - end of Chapter 1
- Quiz for 460: Friday, February 12 in recitation
- Topics 1.4 - 1.8
- 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
- repeated games
- Available in UBLearns>Course Documents>Quizzes at 12:10 PM on
Friday, February 12
- Must be written in dark ink
- PDF of your solution is due in Gradescope by 12:25 PM on Friday,
February 12
- Turn in Problem Set 2: (from the text book), due 02/15/21 in
gradescope by 11:59 PM
- p 33: 2, 5, 6, 10
- p 33: 14, 18
- Note: Problem 18 is a 100-person game, not a 2 player game
- Don't try to draw an outcome table for Problem 18, just explain
why all 100 players voting/not voting is not a Nash equilibrium
- homework should be typed, preferably in LaTeX. 560 Students must use
LaTeX.
- homework should be double spaced
Assignment 3--week of February 15
- Read: 2.3.2 - 2.9
- Quiz for 460: Friday, February 19 in recitation
- Topics: 1.9, 1.10, 2.3, 2.6
- Available in UBLearns>Course Documents>Quizzes at 12:10 PM on
Friday, February 19
- Must be written in dark ink
- PDF of your solution is due in Gradescope by 12:25 PM on Friday,
February 19
- Turn in Problem Set 3: (from the text book), due 02/22/21 in
gradescope by 11:59 PM
- p 33: 16, 17, [19], 20
- problems in brackets should be looked at, not turned in
- Note: in Problem 16 the milk production is given by e^{1 - 1/(Aa)
} , so the A and "a" are both in the denominator
- "Exercise
I"
- p 70: 2, 8
- homework should be double spaced
Assignment 4--week of February 22
- Read: 2.8 - 2.10, 2.1 - 2.3
- Quiz for 460: Friday, February 26 in recitation
- Topics: 2.4, 2.5
- Available in UBLearns>Course Documents>Quizzes at 12:10 PM on
Friday, February 26
- Must be written in dark ink
- PDF of your solution is due in Gradescope by 12:25 PM on Friday,
February 26
- Turn in Problem Set 4: (from the text book), due 03/01/21 in
gradescope by 11:59 PM
- p 70: 1, 3, 5 (draw to a depth of 4), 6
(figure 2.18, p 71)
- 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
Problems 1 and 6 has a typo; second node c should be an e.
Assignment 5--week of March 1
- Read: 2.1 - 2.3, 3.1, 3.3
- Quiz for 460: Friday, March 5 in recitation
- Topics: 2.7, 2.8
- Available in UBLearns>Course Documents>Quizzes at 12:10 PM on
Friday, March 5
- Must be written in dark ink
- PDF of your solution is due in Gradescope by 12:25 PM on Friday,
March 5
- Turn in Problem Set 5: (from the text book), due 03/08/21 in
gradescope by 11:59 PM
- p 70: 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,
totally at random
- p 70: 13, [16, 17], 18 (a hard problem), 20
- Note: you may use the
version of the game from problem 13 in problems 10 and 12, if you
wish
- Note: problem 20 uses figure 2.18, p 71
(diagram has typo: second node c should be an e)
Assignment 6--week of March 8
- Read: 3.1 - 3.6
- Quiz for 460: Friday, March 12 in recitation
- Topics: 2.8, 2.9
- Available in UBLearns>Course Documents>Quizzes at 12:10 PM on
Friday, March 12
- Must be written in dark ink
- PDF of your solution is due in Gradescope by 12:25 PM on Friday,
March 12
- Turn in Problem Set 6: (from the text book), due 03/15/21 in
gradescope by 11:59 PM
Assignment 7--week of March 15
- Read: 3.1 - 3.6
- Quiz for 460: No quiz on Friday, March 19
in recitation
- No problems due this Monday
Assignment 8--week of March 22
- Read: 3.1 - 3.6
- Quiz for 460: Friday, March 26 in recitation
- Turn in Problem Set 7: (from the text book), due 03/29/21 in
gradescope by 11:59 PM
- p 70: 22 - 24
- p 104: [1], 5
Assignment 9--week of March 29
- Read: 3.7 - 4.2
- Quiz for 460: Friday, April 2 in recitation
- Turn in Problem Set 8: (from the text book), due 04/05/21 in
gradescope by 11:59 PM
- 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)
Assignment 10--week of April 5
- Read: 4.3 - 4.6
- Quiz for 460: Friday, April 7 in recitation
- Topics 3.7.1 (product race)
- Turn in Problem Set 9: (from the text book), due 04/12/21 in
gradescope by 11:59 PM
- p 104: [6], 7, 14, 16
- p 104: 18, {{20 skipping duel}}
- p 104: 31 - 33
Assignment 11--week of April 12
- Read: 4.6- 4.9
- Quiz for 460: Friday, April 16 in recitation
- Topics 4.1 - 4.3, 4.5.2
- plus Gale's Roulette (3.11.31, 33)
- Turn in Problem Set 10: (from the text book), due 04/19/21 in
gradescope by 11:59 PM
- Exam II: Wednesday, April 21
Assignment 12--week of April 19
- Read: 6.2 - 6.5
- Quiz for 460: NO QUIZ on Friday, April 23 in
recitation
- Turn in Problem Set 11: (from the text book), due 04/26/21 in
gradescope by 11:59 PM
Assignment 13--week of April 26
- Read: 7.1 - 7.5
- Quiz for 460: Friday, April 30 in recitation
- Turn in Problem Set 12: (from the text book), due 05/03/21 in
gradescope by 11:59 PM
- p 168: 10
- Note for #10: Use figure 5.15 at bottom of p 169.
- p 207: 1, 8, 9
Exam I
- When: Wednesday, March 17, 9:10 AM, zoom proctored,
details will be forthcoming
- Covers: Through 2.9.3 (skip 2.2.1, 2.2.2, 2.3.1)
- including
homework assignments and the corresponding material on the
lecture slides/notes
- includes definition of strategy in perfect info, no chance move
extensive form games
- includes mathematical definition
of Nash equilibrium in n-player game
- includes Pareto improvement
(see notes) and Pareto efficiency
- Format: 5 problems or "show
that"s
- UB ID card must be shown to gain admittance to exam
- Calculators: Only
non-programmable, non-graphing, non-alphanumeric are allowed on exams
- Notes: None
- Internet resources: None are allowed--not to solve
problems, to do problems, or to check solutions
- Collaboration: None. This is to be your own,
individual work
- Exam time: available at 09:10 AM on Wednesday, March
17
- Due in Gradescope: 10:10 AM on Wednesday, March 17
- Submit in black or blue ink handwritten only
- Be sure to match each
problem in Gradescope to the page in your work where the problem can
be found
- E.g., if problem 3 is on page 4, indicate this to Gradescope
Exam II
- When: Wednesday, April 21, 9:10 AM, zoom proctored,
details will be forthcoming
- Covers: 2.1 - 2.3, 3.1 - 4.6
- including
homework assignments and the corresponding material on the
lecture slides/notes
- including the homework,
which has interesting examples not covered in the text
- Format: 4 or 5 problems or
"show that"s
- UB ID card must be shown to gain admittance to exam
- Calculators: Only
non-programmable, non-graphing, non-alphanumeric are allowed on exams
- Notes: None
- Internet resources: None are allowed--not to solve
problems, to do problems, or to check solutions
- Collaboration: None. This is to be your own,
individual work
- Exam time: available at 09:10 AM on Wednesday, April
21
- Due in Gradescope: 10:10 AM on Wednesday, April 21
- Submit in black or blue ink handwritten only
- Be sure to match each
problem in Gradescope to the page in your work where the problem can
be found
- E.g., if problem 3 is on page 4, indicate this to Gradescope