Dixit and Skeath, Games of Strategy, Second Edition 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 5% point penalty compounded daily. For example, an assignment that is 1 day late will yield 95% of its on-time value, 7 days late yields 70% of on-time value, and 14 days late yields 49% of on-time value. 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
Short Assignment 12 worth 10 points due at the Final Exam.
Here are the Practice Final Solutions.
Assignment 11 due Wed May 10. The Practice Final is worth 20 points of extra credit if submitted at end of class on Fri May 12. Solutions will be distributed at the end of class on Wed May 10. Assignment 10 due Wed May 3.
In class of Fri Apr 28 we completed a Prisoner's Dilemma Worshop.
Assignment 9 due Wed Apr 26.
Here is the Practice Midterm 2 Solution Assignment 8 due Wed Apr 5
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.
Print out a copy of Practice Midterm 2 and attempt to solve the problems without referring to your notes or the book. The solutions will be released in-class at the review of Mon Apr 3. Assignment 7 due Wed Mar 29. Assignment 6 due Wed Mar 22. Lecture Notes for Mon Mar 13. Assignment 5 due Wed Mar 15.
Here is the Practice Midterm 1 Solution. Assignment 4 due Wed Mar 8.
Print out a copy of Practice Midterm 1 and attempt to solve the problems without referring to your notes or the book. The solutions will be released in-class at the review of Mon Mar 6. Assignment 3 due Wed Mar 1
I. Chapter 3, #10(a)-(c)
II. Chapter 4, #1, 2, 3(a)(c)(d), 6
III. 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 22
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) Game Tree Handout for class of Mon Feb 13.
A revised and more detailed course calendar is now available.
Assignment 1 due Wed Feb 15
I. Develop your own examples illustrating each of the following topics. (Section 1.2 of Dixit and Skeath may be helpful.)
