MTH 460/560--Theory of Games--Homework Assignments

Homework: due Mondays in lecture

Quiz (460 only): Fridays in recitation

Exams:

• Exam I: Friday, March 6
• Exam II: approx Friday, April 24 Note change in date
• Final Exam: Wednesday, May 13, 2020, 8:00 - 11:00, in Math 150 Not exactly
  

Office Hours: Mon, 12:30 - 1:20 PM; Wed, 1:30 - 2: 20 PM,  and by appointment 

Course Material--UBlearns > Course Documents

• 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.

Final Exam

• When: Wednesday, May 13, available in the morning. Due in Gradescope by midnight on Friday, May 15.
• preferably typed in LaTeX or Word
• one page per question is ideal
• Be sure to assign a page or pages to each question in Gradescope. If you do not know how to do this, here is a link that might be helpful:
• https://www.dur.ac.uk/mathematical.sciences/teaching/gradescope/
• Note that you submit your exam as if it were homework.
• You can type your name when you sign the integrity pledge if the rest of your exam is typed
• Where: in the cloud
• Covers: Through 2.8 (skip 2.2.1, 2.2.2, 2.3.1),  2.9, 3.1 - 3.7.1, 4.1 - 4.8.1, 5.1, 5.2 (skip 5.2.1), 6.1. skip 6.1.1 except last paragraph, 6.2 - 6.5
•  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 460 Lec 36 2020_04_24
• Format: 1 - 3 definitions or statements of result or questions based on definitions, 6 - 10 problems
• No books, notes, internet resources (except for LaTeX or Word), consultation, collaboration via any method
  
• No alphanumeric/programmable/graphing calculators and or computer algebra systems allowed

Coming Attractions (tentative list of upcoming assignments):

Assignment 1--week of January 27

• Recitation: will meet on Friday, January 31 at 8:00 AM in Math 150
• Read: Chapter 1, through 1.7
• Quiz for 460: Friday, January 31 in recitation
• Topics 1.1 - 1.4
• Turn in Problem Set 1: (from the text book), due 02/03/20 in class
• 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 3

• Read: Chapter 1.7-end of chapter 1
• Quiz for 460: Friday, Febraury 7 in recitation
• Topics 1.5 - 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
• repeated games
• Format: one definition or statement, one problem
• Turn in Problem Set 2: (from the text book), due 02/10/20 in class
• p 33: 2,  5, 6, 10
• p 33:  14, 18
• Note: Problem 18 is a 100-person game, not a 2 player game
• For 18: Don't try to draw an outcome table, 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
• LaTeX resources: UBLearns>Course Documents

Assignment 3--week of February 10

• Read: Chapter 2.3 - 2.8
• Quiz for 460: Friday, February 14 in recitation
• Topics 1.10 - 1.11, 2.3.2, 2.3.3
• Format: one definition or statement, one problem
• Turn in Problem Set 3: (from the text book), due 02/17/20 in class
• p 33: 16, 17, [19], 20 (note; #18 was removed from assignment as it had been assigned last week)
• 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"
• Please indicate on your homework which section (460 or 560 you are in)
• Make sure your homework is double spaced

Assignment 4--week of February 17

• Read: Chapter 2.3 - 2.9
• Quiz for 460: Friday, February 21 in recitation
• Topics:  2.3 - 2.6
• Format: one definition or statement, one problem
• Turn in Problem Set 4: (from the text book), due 02/24/20 in class
• 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.
• p 70: 8 (explain your reasoning)
• p 70: 2, 3

Assignment 5--week of February 24

• Read: Chapter 2.3 - 2.9
• Quiz for 460: Friday, February 28 in recitation
• Topics:  2.5, 2.7, 2.8
• Format: one definition or statement, one problem
• Turn in Problem Set 5: (from the text book), due 03/02/20 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
• Exam I, Friday, March 6. Covers through all of 2.8

Assignment 6--week of March 2

• Read: Chapters 3.1 - 3.3
• Quiz for 460: No quiz Friday, March 6 in recitation
• Topics: 
• Format: one definition or statement, one problem
• Turn in Problem Set 6: (from the text book), due 03/09/20 in class
• p 70: 18
• p 70: 20, 21, 26

Assignment 7--week of March 9

• Read: Chapters 3.4 - 3.6
• Quiz for 460: Friday, March 13 in recitation
• Topics: 2.9, 3.1, 3.2
• Format: one definition or statement, one problem
• Turn in Problem Set 7: (from the text book), due 03/23/20 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

Assignment 8--week of March 23

• Read: Chapters 3.4 - 3.6
• Quiz for 460: no quiz this week
• Topics:
• Format: one definition or statement, one problem
• Turn in Problem Set 8: (from the text book), due 03/31/20 in gradescope
• 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 9--week of March 30

• Read: Chapters 3.7, 4.1, 4.2
• Quiz for 460: Available Friday
• Topics: 3.3 - 3.7
• Format: one definition or statement, one problem
• Turn in Problem Set 9: (from the text book), due 04/06//20 in gradescope
• p 104: [6], 7, 14, 16
• p 104: 18, {{20 skipping duel}}
• p 104: 31 - 33
• Read: What was I thinking? The latest reasoning about our irrational ways.
• A related interesting article: The Advantages of Closing a Few Doors

Assignment 10--week of April 6

• Read: Chapters 4.3-4.5
• Quiz for 460: Available Friday
• Topics: 4.1 - 4.3, 4.5 (including beginning of 4.5.2)
• Format: one definition or statement, one problem
• Turn in Problem Set 10: (from the text book), due 04/13//20 in gradescope
• 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)

Assignment 11--week of April 13

• Read: Chapters 4.6 - 4.8
• Quiz for 460: Available Friday, due by Midnight on Sunday
• Topics: 4.5
• Format: one definition or statement, one problem
• Turn in Problem Set 11: (from the text book), due 04/20//20 in gradescope
• p 136: 11, 12, 14, 15, 22

Assignment 12--week of May 4

• Read: Chapters 6.2 - 6.5
• Quiz for 460: no quiz this week
• Turn in Problem Set 12: (from the text book), due 05/08//20 in gradescope
• p 207: 1 - 3, 8, 9, 20
• 2 is a hard problem
• 3 is a harder

Exam I

• When: Friday, March 6  at 9:00 AM in Math 150
• Covers: Through 2.8 (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 effciency
  
• 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, April 24, released tentatively at noon
• Due in Gradescope: Sunday, April 26 at 11:59 PM
• Covers: Sections 2.9, 3.1 - 3.7.1, 4.1 - 4.8.1, 5.1, 5.2 (skip 5.2.1)
• including the corresponding material on the lecture notes
• including the homework, which has interesting examples not covered in the text
• including the strategic form of an extensive form game with imperfect information and chance moves
• including all the VNM material
  
• Format:
• designed to be a sixty minute exam
• preferably typed in LaTeX or Word
• 1 or 2 definitions or statements of result, 4 to 6 problems or "show that"s
• No books, notes, internet resources (except for LaTeX or Word), consultation, collaboration via any method
  
• No alphanumeric/programmable/graphing calculators and or computer algebra systems allowed