MTH 460/560--Homework Assignments

Note: problems in brackets [ ] are to be done, but not turned in.

• Exam I: Wednesday, February 29 completed
• Exam II: Wednesday, April 18 completed
• Final Exam: Friday, May 4, 11:45 AM - 2:45 PM in NSC 210 [note change in room]

• Convex Hull
• Basic Principle of Mixed Strategies
• etc.

Final Exam

• When: : Friday, May 4, 11:45 AM - 2:45 PM in NSC 210 [note change in room]
• Covers: Chapters 1-7.4.2 (skip 3.8)
• Plus: Convex Hull, Basic Principle of Mixed Strategies (both in course materials UBLearns)
• Includes: The method of section 5.2.2; the method and justification for finding security levels  by linear programming
• Format: 1 or 2 definitions or statements of result, 6- 9 problems
• Required: Non-programmable, non-graphing, non-alphanumeric calculator
• Office Hours: Wednesday, May 2, 3:00 PM; Thursday, May 3, TBA
• Review Session: Wednesday, May 2, 6:45 PM in Math 250

Coming Attractions (tenatative list of upcoming assignments):

• TBA

Assignment 1--Due Wednesday, January 25 [usually due Mondays]:

• Recitation for 460: no recitation on Friday, January 20
• p 33: 2, 3, [5], [6], 7, 9, 10 (for weakly dominant--see bottom of p 23)
• Quiz for 460: no quiz this week (January 20)

Assignment 2--Due Monday, January 30:

• Quiz for 460: Friday, January 27 in recitation. Topics: Chapter 1 [including "Exercise I"]
• Format for quizzes: 1 statement or definition, 1 problem
• p 33:  14, 16-18, [19], 20  Note: Problem 18 is a 100-person game, not a 2 player game
• "Exercise I" (turn this in also)

Assignment 3--Due Monday, February 6:

• Quiz for 460: Friday, Feb 3 in recitation. Topics: 2.3.2-2.4
• p 70: 1-3, 5 (draw to a depth of 4), 6 (figure 2.18,  p 71), 8 (explain your reasoning)
• Note: Fig. 2.18 for Problem 1 has a typo; second node c should be an e.
• Note: Problem 8: "do the same"--who would win (and why) for 2^n  - 1 piles and describe play for 2^n  -1 piles where n = 3

Assignment 4--Due Monday, February 13:

• Quiz for 460: Friday, Feb 3 in recitation. Topics: 2.5-2.8.2
• p 70: 10 (3 x 3 only; explain), 12 (do Beck's Hex 3 x 3 only, but explain "playing anywhere" in general), 13, [16, 17]
• Note: Problem 12: "playing anywhere" means that you can place the marker arbitrarily
• Note: you may use the version of the game from problem 13 in problems 10 and 12, if you wish
• p 70: 18, 19
• Note: 18 is hard--related to finding a sequence of 0's and 1's that doesn't repeat, but does have a pattern
• p 70: 20, 21, 26
• Note: for a definition of Tactical/Strategic voting (Problem 26) see first lines of wikipedia article
• Read:  Section 3.1 for Monday

Assignment 5--Due Monday, February 20:

• Quiz for 460: Friday, Feb 17 in recitation. Topics: mixed strategies, information sets, strategic form, 3.1-3.4
• p 70: 22-24
• p 104: [1], 5, 8, 9-13 (#8 has been added to this assignment)
• 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

Assignment 6--Due Monday, February 27:

• Quiz for 460: Friday, Feb 24 in recitation. Topics: 3.5 - 3.7.1
• p 104: [6], 7, 14, 16, 18, 31-33, 20 (if we get to this on Friday)

Assignment 7--Due Monday, March 5:

• Quiz for 460: No quiz on Friday, Mar 2 in recitation.
• p 104: 21, 23, 24
• Read: What was I thinking? The latest reasoning about our irrational ways.
• A related interesting article: The Advantages of Closing a Few Doors

Assignment 8--Due Monday, March 19:

• Quiz for 460: Friday, Mar 9 in recitation. Topics:  Chapter 4.1 - 4.3., 4.5.1, 4.5.2
• p 136: 3-7, 9-11 (don't read too much into Problem 10; it's not as complicated as Section 4.3.1)
• Misprint 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 9--Due Monday, March 26:

• Quiz for 460: Friday, Mar 23 in recitation. Topics:  what we've been talking about
• p 136: 12, 14, 15, 17, 23

Assignment 10--Due Monday, April 2:

• Quiz for 460: Friday, Mar 30 in recitation. Topics:  4.5.3-5.2
• p 168: 1-3, 8, 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 answer.
• Review vectors, matrices, transpose
• p 168: 5 (should be "figure 5.16 top of 171"), 9

Assignment 11--Due Monday, April 9:

• Quiz for 460: Friday, April 6 in recitation. Topics:  5.3 - 5.5, 6.1
• p 168: 15-17, 19
• Note: the very first part of problem 15a is not really a question. Just ignore it.
• p 207: 2-4 Note: 3 is a hard problem. You might want to start working on it early.
• Note for problem 4: Strategies are: stay out, bid 0, bid 1, ..., bid 1M. Assume that  c  is is in the thousands.

Assignment 12--Due Monday, April 16:

• Quiz for 460: Friday, April 13 in recitation. Topics:  6.2 - 6.5.1
• p 207: 8, 9
• p 207: 18-20

Assignment 13--Due Monday, April 23:

• Quiz for 460: no quiz on Friday, April 20 in recitation.
• p 207: 22-26 Note: 26 is a hard problem. You might want to start working on it early.
• Convex Hull: Problems 1-3 (turn these in)
• p 207: 28, [30] (will discuss this more on Friday)

Assignment 14--Due Monday, April 30:

• Quiz for 460: Friday, April 25 in recitation, topics  TBA
• p 246: 2-7
• Note: for 7, there is a misprint. Should be minimize max for "s in S" and not for "s in t".
• p 246: 10, [11], 13, [14], 15, [16], [17], 37 (include a printout)
• Note: for 37, Theorem 7.9 says that the security value is the value of the game, so can solve the games by the method descsribed in class and the book
• Note: for 11, assume that M is the payoff matrix for player I in a zero sum game. The question is, what are II's security levels, etc?]

Exam I

• When: Wednesday, February 29 at 11:00 AM in Math 250
• Covers: Through 3.7.2 (with some topics omitted as in the homework assignments)
• Format: 1 definition or statement of result, 4 problems
• Calculators: Only non-programmable, non-graphing, non-alphanumeric are allowed on exams

Exam II

• When: Wednesday, April 18 at 11:00 AM in Math 250
• Covers: 4.1 - 6.5.1(with some topics omitted as in the homework assignments)
• Format: 1 definition or statement of result, 4 problems
• Calculators: Only non-programmable, non-graphing, non-alphanumeric are allowed on exams