GAME THEORY AND APPLICATIONS


MAP 4180, Section 01, Fall 2016

(Class #05060)

Game Theory and Applications will be taught from the perspective of an applied mathematician, i.e., it will focus on game-theoretic modelling (as opposed to rigorous proofs of existence and uniqueness theorems). The course will cover, in a unified way, both classical and evolutionary game theory, and should be of interest not only to mathematics majors but also to students in the life and social sciences
Course page: ON CAMPUS: http://www.math.fsu.edu/~mesterto/GameTheory.html (this page)
OFF CAMPUS: http://www.math.fsu.edu.proxy.lib.fsu.edu/~mesterto/GameTheory.html (with your FSUID username and password)
Professor: Dr M-G
Office: 202B Love
Office hours: Please click here. Note that office hours are primarily for personal matters that cannot be addressed in class (as opposed to tutorial help, for which see under Course format and How to study below)
Phone:(850 64)4 2580
Main website: Professor M-G's Home Page    Email:
Course goal:To introduce game theory and some of its applications
Class meets: In 106 LOV on Mondays, Wednesdays and Fridays at 2:30—3:20 p.m.
Text: No required text
Credit: 3 semester hours. Mathematics majors may take MAP 4180 as an elective counting toward credit for graduation
Syllabus: Topics selected from the following components:
Noncooperative games (including Nash equilibrium and other solution concepts)
Population games (including evolutionary stability)
Cooperative games in strategic form
Cooperative games in characteristic function form
Cooperation and the prisoner's dilemma
Applications (including further discrete or continuous population games)
Prerequisites:
(i) MAC 2313, MAS 3105, STA 4321, MAP 2302; or Professor M-G's consent
(ii) self-motivation and industriousnes
(iii) patience—an underappreciated but essential virtue for an applied mathematician
My philosophy of learning is perhaps best expressed by the green curve in the diagram below:
 
ALTERNATIVE THEORIES OF LEARNING VERSUS PAIN
For further details, please click here.
Communication: I will send email to your FSU email account on a regular basis. It is your responsibility to check it regularly (or arrange to have my messages forwarded, if you prefer to read your email elsewhere)
Your name:
      I don't know who you are, but because everything works so much better when I do, I would like to learn your name as soon as possible. So, please take a sheet of card stock (or even paper), fold it in half, write your name in large letters on one side and stand it up on your desk so that I can see it. (Write what you want me to call you: if you're a John who likes to be called Fred or a Jane who likes to be called Sue, write Fred or Sue, not John or Jane.) Please bring your nameplate to every class until I have finally learnt your name (which will take significantly longer than it used to take when I started out)
Course format: Lectures and discussion, with occasional periods devoted entirely to (interactive) problem solving. Questions may be asked at any time—and should be, if there's anything you don't understand.
    The course will be based on a preliminary draft of the 3rd edition of my Introduction to Game-Theoretic Modelling, of which a section or two will form the basis of each lecture. After each period I will edit this draft (e.g., to correct mistakes I discover during class or to rework some of the material) and then email the resulting lecture to you as a PDF file. I will also post the file here. So in class you should focus on understanding what we are actually doing—as opposed to on writing it all down, since in effect I will do that for you!
    Please note that the lectures are copyrighted material, sent to you on the understanding that they are solely for your personal use and not to be shared (with anyone who is not registered for the course)
Homework: After each period you should read the associated lecture carefully and attempt any related problem. Sometimes a lecture will go a little beyond what we actually had time for in class, in order to advance us to a more natural break point (by adding material that is straightforward for you to read all by yourselves). At other times, a single lecture will cover several periods, in which case, I will keep sending a PDF file that supersedes the previous one, until eventually you have the whole lecture in a single file. To the greatest extent possible, we will attempt not to introduce new material until everyone understands what has gone before; however, the extent to which we succeed in this regard depends critically on how much you cooperate by doing all of your homework before the following period. (Needless to say, when you read a lecture, you should always keep pencil, paper and calculator handy, so that you can fill in steps by yourself where necessary.)
Grades: Will be based on five written assignments (20% apiece), for all of which you must use ink (if you make a mistake when writing in ink, just cross out neatly and correct). Note that quality of presentation is extremely important, and so there will be penalties (commensurate with degree of infraction) for badly presented work. It is not enough merely to produce an answer. The method by which you obtain it must be sound and clearly demonstrated: Show all necessary steps in your method, with enough comments or diagrams to convince that you thoroughly understand. On the other hand, don't turn in acres and acres of verbiage: although it is generally better to err on the side of saying too much than on the side of saying too little, saying far too much is usually an indication that you don't really know what you are talking about and are trying to hide it with words.
    Precise cut-off points for A, B and C will be determined by the distribution of grades at the end of the semester, but are likely be in the vicinity of 90%, 80% and 70%, respectively. In borderline cases, a smaller number of completely correct solutions will carry more weight than a proportionate number of fragmentary answers; later scores will carry more weight than earlier scores; and a record of active participation in class will carry more weight than a record of passive attendance. Plus or minus grades may be assigned in a manner consistent with standard University practice.
    Please note that partial credit will be awarded only when part of a solution is completely correct—not when all of a solution is partially correct, whatever that means, if anything. A score for a question worth 10 points should be interpreted as follows:
10 Practically perfect
9 Still very good, but lacking—or wrong about—a significant detail
8 Still good, but lacking—or wrong about—significant details
7 Minimally satisfactory. You have—just—managed to demonstrate that you basically understand and are at least capable of getting all details correct (although it clearly did not happen this time)
6 A grade that will not be given
5 Half right in some appropriate sense (e.g., there were two parts, each worth 5 points, and your first part was practically perfect)
1-4 Not even half right and showing little understanding, but some degree of positive effort
0 Zero effort, or submitted in pencil
Also note that a grade of I will not be given to avoid a grade of F or to give additional study time. Failure to process a course drop will result in a course grade of F
Attendance policy: You are expected to attend class regularly, and bear the full responsibility for learning anything covered during any class that you miss. On the other hand, it would be extremely anti-social to attend class if you either have, or are coming down with, a contagious disease. Please keep me apprised (by email) of any illness or other emergency, so that I can make any necessary adjustments (and please make friends within the class as soon as possible if you haven't done so already, so that there is someone you can call upon to borrow notes if the need should ever arise)
Etiquette: You are firmly bound by Florida State University's Academic Honor Code. Briefly, you have the responsibility to uphold the highest standards of academic integrity in your own work, to refuse to tolerate violations of academic integrity in the University community, and to foster a high sense of integrity and social responsibility on the part of the University community. Even more briefly, you must neither cheat nor enable others to cheat. The penalties for violations can be severe. Please carefully read the section in the FSU Student Handbook on the Honor Code and official procedures for dealing with students who violate it. Although you may discuss assignments with others in general terms, the solutions you present must be your very own work ("in general terms" means that discussion is oral and nothing is copied down). If you are in any doubt at all as to what constitutes acceptable behavior in this regard, you should ask me for clarification.
    You are also bound by the ordinary rules and customs of polite behavior that prevail in a civilized society. (In particular, you are not allowed to use a cell phone or otherwise have private conversations with others during class; and you are not allowed to create disturbances through arriving late or leaving early.)
How to study: It is important that you keep up with the course from the very beginning, always attempting as many as possible (preferably all) of any homework problems. If you get stuck, then send me a question by email. As soon as I possibly can, which might be as soon as within half an hour, but might also be a day or two later (I have a life, too, you know), I will reply—not to you, but rather to the class alias (after carefully concealing your identity, just in case you are inexplicably bashful about being perceived as smart enough to ask a question).
    Note, however, the following. First, you must identify yourself (i.e., you remain anonymous to the other students in the class, but not to me) in the body of your message (because your username does not identify you to me, and I don't reply to anonymous email). Second, you should be as specific as possible in describing your difficulty: the more precisely you identify how you got stuck, the more helpful my reply is likely to be
Disabilities: If you have a disability requiring academic accommodations, then not only should you register with the Student Disability Resource Center (SDRC), but also you should bring me written confirmation from SDRC during the first week of class

ALL SYLLABI ARE REQUIRED TO INCLUDE THE FOLLOWING STATEMENTS

University Attendance Policy:
Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holy days, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.

Academic Honor Policy:
The Florida State University Academic Honor Policy outlines the University's expectations for the integrity of students' academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty members throughout the process. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to ". . . be honest and truthful and . . . [to] strive for personal and institutional integrity at Florida State University." (Florida State University Academic Honor Policy, found at http://fda.fsu.edu/Academics/Academic-Honor-Policy.)

Americans With Disabilities Act:
Students with disabilities needing academic accommodation should:
(1) register with and provide documentation to the Student Disability Resource Center; and
(2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class.

This syllabus and other class materials are available in alternative format upon request.

For more information about services available to FSU students with disabilities, contact the:

Student Disability Resource Center
874 Traditions Way
108 Student Services Building
Florida State University
Tallahassee, FL 32306-4167
(850) 644-9566 (voice)
(850) 644-8504 (TDD)
sdrc@admin.fsu.edu
http://www.disabilitycenter.fsu.edu.proxy.lib.fsu.edu/

RECOMMENDED LANGUAGE FOR SYLLABI:

Free Tutoring from FSU

On-campus tutoring and writing assistance is available for many courses at Florida State University. For more information, visit the Academic Center for Excellence (ACE) Tutoring Services' comprehensive list of on-campus tutoring options—see http://ace.fsu.edu.proxy.lib.fsu.edu/tutoring or contact tutor@fsu.edu. High-quality tutoring is available by appointment and on a walk-in basis. These services are offered by tutors trained to encourage the highest level of individual academic success while upholding personal academic integrity.

Syllabus Change Policy

"Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.''


Lectures

  1. Overview
  2. Community Games
    1. A motorist's dilemma
    2. Optimal reaction sets. Nash equilibria
    3. A motorist's trilemma
    4. A continuous game of prices
    5. A three-player game
    6. Max-min strategies
    7. Commentary
    8. Exercises
      
  1. Population Games
    1. Crossroads as a population game
    2. Evolutionarily stable strategies
    3. Crossroads as a continuous population game
    4. Hawk-Dove games
    5. More on evolutionarily stable strategies
    6. A continuous Hawk-Dove game
    7. Multiple deviation. Population dynamics
    8. Discrete population games. Multiple ESSes
    9. Continuous stability
      
  1. Cooperative Games in Strategic Form
    1. Unimprovability: group rationality
    2. Necessary conditions for unimprovability
    3. The Nash bargaining solution
    4. Independent versus correlated strategies
      
  1. Characteristic Function Games
    1. Characteristic functions and reasonable sets
    2. Core-related concepts
    3. A four-player CFG
    4. A coreless game
    5. The nucleolus
    6. An improper game
    7. The Shapley value

    Appendix A

Solutions or Hints for Selected Exercises

Exercise 1.02
Exercise 1.05
Exercise 2.09
Exercise 2.10

Assignments

Assignment 1 (due at revised deadline of 2:30 p.m. on Wednesday, September 28, 2016)
Assignment 2 (due at revised deadline of 2:30 p.m. on Wednesday, October 19, 2016)
Assignment 3 (due at revised deadline of 2:30 p.m. on Wednesday, November 09, 2016)
Assignment 4 (due at revised deadline of 2:30 p.m. on Monday, November 28, 2016)
Assignment 5 (due at 3:20 p.m. on Friday, December 09, 2016)

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