Games of Strategy, Second Edition Dixit and Skeath W.W. Norton & Company, c2004.
Homework: There will be a weekly homework assignment due at the beginning of class on Wednesdays. I expect you to write a complete solution to every assigned problem. If you get stuck on a problem, or if you are not confident in your solution, please confer with fellow students, a tutor, or come ask me in office hours. Late homework will be accepted with a 30% penalty compounded weekly. For example, an assignment that is late less than 1 week will yield 70% of its on-time value, between 1 and 2 weeks late yields 49% of on-time value, between 2 and 3 weeks late yields 34% of on-time value, and so forth. Missing homework will receive a score of zero. Missing homework will receive a score of zero. Exams: There will be two midterms and a final. Midterm 2 will cover the material after midterm 1. The final exam will be cumulative with an emphasis on the material after midterm 2. Missing an exam will result in an exam score of zero being assigned. Grades: Your grade is based on homework and exams. The weight each component shall receive is as follows: 34% homework average, 22% Midterm 1, 22% Midterm 2, 22% Final Exam. When the final exam score exceeds the lesser of the two midterm scores, the final exam score will replace the lesser of the two Midterm scores. The following distribution will be used to assign course grades: 100-93% = A, 92-90% = A-, 89-86% = B+, 85-83% = B, 82-80% = B-, 79-76% = C+, 75-73% = C, 72-70% = C-, 69-66% = D+, 65-63% = D, 62-60% = D-, Below 60 % = F. Calculators: Calculators are always permitted. Tutoring: The Student Math Center is open every Sunday and Monday from 7-9pm in Galileo 201. Additional tutoring may be requested from the Academic Support Center in Sichel 105. Academic Honesty: The Saint Mary's policies regarding academic honesty detailed in the student handbook apply to this course. I encourage you to work with other students on coursework, but your write-ups should be in your own voice, and consist largely of your own work. Where your argument depends heavily on another's work, say so. Course Calendar: The course calendar details the schedule of coursework, exams and breaks.
Homework and Announcements
Extra Credit Review 3 due at the final exam is worth 10 points of extra credit. Assignment 13 due Wed May 23. Assignment 12 due Wed May 16. Worked Examples for classes of Mon Apr 23 through Wed May 16. Assignment 11 due Wed May 9. Assignment 10 due Wed May 2. Assignment 9 due Wed Apr 25. Extra Credit Review 2 due Wed Apr 25 is worth 10 points of extra credit. Worked Examples for classes of Fri Mar 16 through Wed Apr 18. Assignment 8 due Wed Apr 18
I. Chapter 8, #1, 4(a), 5
II. For each of the games below, determine the strategic effect (if any) of allowing a player to send one message to the other player prior to game play.
(a) The Baseball Pitch game in Chapter 7, #6.
(b) The Old Lady game in Chapter 7, #5. Assignment 7 due Wed Apr 11. Assignment 6 due Wed Mar 28. Lecture Notes for class of Mon Mar 19 and Wed Mar 21. Assignment 5 due Wed Mar 21. Practice Midterm 1 due Wed Mar 14 is worth 10 points of extra credit.
Print out a copy of the Demostration Midterm 1 Solutions and compare with your solutions, both for the final answers and the justifications given. Assignment 4 due Wed Mar 14.
Print out a copy of Demonstration Midterm 1. Refer to it periodically to see which problems you can solve. You might already be able to solve 1-5! Solutions will be made available in class on Mon March 12. Assignment 3 due Wed Mar 7
I. Chapter 4, #1, 2 (omit the part that askes you to "Verify your answers by using the minimax method"), 3(a)(c)(d), 6
II. Consider the cola industry, in which Coke and Pepsi are the two dominant firms. (To keep things simple, just forget about all the others.) The market size is $8 billion. Each firm can choose whether to advertise. Advertising costs $1 billion for each firm that chooses to do so. If one firm advertises and the other doesn't, then the former captures the whole market. If both firms advertise, they split the market 50:50 and pay for the advertising. If neither advertises, they split the market 50:50 but without the expense of advertising.
(a) Write down the payoff table for this ad game.
(b) Write down the game tree for this ad game (assume that it is played sequentially), with Coke moving first and Pepsi following. Determine rollback strategies and payoffs.
(c) Write down the game tree for this ad game (assume that it is played sequentially), with Pepsi moving first and Coke following. Determine rollback strategies and payoffs.
(d) Is there a move order advantage? Why or why not? Assignment 2 due Wed Feb 28
I.Chapter 3, Find rollback strategies and payoffs in the game trees of #2
II. Chapter 3, #4,5,9
III. The description of the Survivor Immunity game on p.75 gives various numerical probability values which are then assigned to the relevant branches of the game tree on p.74. Suppose that Rich's increases his estimation of Rudy's strength, meaning that Rich decides that Rudy is harder to beat in the Immunity game than he previously thought. In particular, suppose Rich estimates the probability of an Immunity Challenge win as follows:
If Rich chooses to give up, Kelly has a 70% chance of winning, and Rudy has a 30% chance of winning.
If Rich choose to continue, Rich has a 40% chance of winning, Kelly has a 45% chance of winning, and Rudy has a 15% chance of winning.
(a) Relabel the branches of the Survivor Immunity game tree with the probability values given above.
(b) Rollback the Survivor Immunity game tree in (a) to determine if Rich should Give Up or Continue.
(c) In the original Survivor scenario described in section 3.7, could Kelly have won? What should Kelly have done? Justify your answer using a Survivor Immunity game tree where the initial node belongs to Kelly instead of Rich and the payoffs at the bottom are Kelly's.
IV. Chapter 3, #10(a)-(d) Assignment 1 due Wed Feb 21
Chapter 2 #1, 2, 3
Chapter 3 #1, 2
