Math 4390/5390 Game Theory

Math 4390/5390 Game Theory

Spring 2015 Syllabus

Instructor: Burt Simon Course dates/times: MW 5:00-6:15

Office: Academic Building, Room 4209 Course location: NC 1324

Office Hours: MW 2:00-4:00, or by appt. Email:

Course Description

Game theory is a collection of mathematical models of interactions between two or more agents. The agents are often assumed to be perfectly rational, but not always. The theory aims to answer questions like (i) How will rational agents behave when they have to take other rational agents into account? (ii) What is a “fair” outcome of a game? (iii) What is likely to happen when successful strategies proliferate in a population at the expense of less successful strategies? Applications of the theory can be found in economics, political and military science, moral philosophy, and evolutionary biology. This course covers the basic ideas in game theory that model strategies for rational play, fairness, and evolutionary change.

Prerequisites

Recommended: Probability (e.g., Math 3800 or 4810), Differential equations (e.g., Math 3200 or 3195), and some programming experience (e.g., Matlab).

Textbooks and Reference Material

Game theory is a very broad field and there does not appear to be any single text that covers (at the appropriate level) the mix of topics I want to cover in this course. In my lectures I will therefore borrow from a variety of books, and add some of my own material as well. I do not expect students to purchase all of the books I will use, and in fact, none of them are strictly necessary. I think Herb Gintis’ book is excellent, as is Martin Nowak’s, so if you want books to read and keep, I suggest those. The “Idiot’s Guide” was used recently as a text for this course (and is not nearly as bad as it sounds), and Davis’ book was also once used as a text.

Recommended Textbooks:

1.  Game Theory Evolving, 2nd ed., by Herbert Gintis (2009)

2.  Evolutionary Dynamics, by Martin Nowak (2006)

Additional References

1.  The Complete Idiot’s Guide to Game Theory, by Edward C. Rosenthal (2011)

2.  N-Person Game Theory, by Anatol Rapoport (1970)

3.  Game Theory, A Nontechnical Introduction, by Morton Davis (1970)

Course Objectives

·  Present basic models of conflict and cooperation.

·  Present solution techniques for simple games based on models of rational play and fairness.

·  Present models of the evolution of game strategies in non-rational agents.

·  Present applications of the theory in economics, political and military science, and biology.

Class Website

Click on the link to our class from www.math.ucdenver.edu/~bsimon

Assignments, Exams, and Grading

·  Your primary source of information for this course will be the lectures. I will not take attendance, but you should make a point of attending every class.

·  Homework will be assigned (approximately) weekly. The assignments will be posted on the class website. Usually assignments will be assigned on Monday or Tuesday and due at the beginning of class on the following Monday.

·  Students are encouraged to work together on homework assignments.

·  We will discuss homework problems during class when they are due, so sets turned in late cannot receive full credit. You can email assignments to me, but I prefer hard copies.

·  There will be a midterm exam and final exam. The midterm will be a traditional in-class exam. The format for the final exam will be determined later.

·  Graduate students (taking 5390) will do a project related to course material, due at the end of the semester. Undergraduates (taking 4390) will be encouraged, but not required, to also do a project. Time will be set aside in the last couple of weeks for presentations and discussions.

·  Your grade will be based on Homework (at least 20%), Exams and/or Projects (at least 40%), and other evidence of achievement, like class participation, undergrad project presentations, and work in addition to what is assigned (up to 40%). The grade you receive for the course will be based on my best estimate of how much Game Theory you learned, along with test and homework scores.

Tentative Course Schedule

Class dates Material Covered

January 21 Introductory examples

January 26, 28 Utility theory

References: Gintis, Chapters 2 (advanced) and 3;

Idiot’s Guide, Chapter 18; Davis, Chapter 4

February 2, 4 Two-person zero-sum games

Minimax Theorem, examples

References: Davis, Chapters 2, 3; Idiot’s Guide, Chapter 3

February 9, 11 Non-zero-sum games, Nash equilibrium (pure, mixed)

References: Gintis, Chapters 4, 5, 6; Davis, Chapter 5;

Idiot’s Guide, Chapters 4, 5

February 16, 18 More non-zero-sum games, Classic games,

Prisoner’s dilemma, Ultimatum, Snowdrift

February 23, 25 Repeated games, Repeated prisoner’s dilemma,

Experiments with humans, Axelrod’s tournament

March 2, 4 Review and Midterm Exam

March 9, 11 N-person games, Von Neumann Morgenstern Solutions,

Core of a game

Reference: Rappaport, Chapter 4

March 16, 18 Models of fairness, Cooperative games, Shapley value

References: Idiot’s Guide, Chapters 9-12,

Rappaport, Chapters 5,6

March 23-27 SPRING BREAK

March 30, April 1 Evolutionary Games, Evolutionary Stable Strategy (ESS)

References: Gintis, Chapters 9. 10,

Idiot’s Guide, Chapters 17 and 22

April 6, 8 Replicator dynamics, Reactive strategies for PD

Reference: Nowak, Chapters 4,5

April 13, 15 Population Dynamics for Rock-Paper-Scissors

And other games

References: Gintis, Chapters 11, 12

April 20, 22 Catch-up (if necessary)

Project presentations

April 27, 29 More project presentations

May 4, 6 Review, and more project presentations

May 11-15 Finals week.

Spring 2015 CLAS Academic Policies
The following policies, procedures and deadlines pertain to all degree-seeking students in the College of Liberal Arts and Sciences (CLAS) and are aligned with the Official University Academic Calendar. Please also see you advisor if you have questions or concerns.
·  Schedule verification: It is each student’s responsibility to verify online that his/her official registration and schedule of classes is correct before classes begin and prior to the drop/add deadline. Failure to verify schedule accuracy is not sufficient reason to justify a late adds or drops.
·  E-mail: Students must activate and regularly check their official CU Denver e-mail account for university related messages. Those who forward email should check CU Denver e-mail regularly for messages not automatically forwarded.
·  Waitlists:
o  Students are automatically notified if they are enrolled in a class from a waitlist via their official CU Denver email account.
o  Students are not automatically dropped from a class if they never attended, stopped attending, or do not make tuition payments, though instructors may request administrative drops.
o  Waitlists are purged after the 1st week of classes.
·  Late adds (after 4 February) will be approved only when circumstances surrounding the late add are beyond the student’s control. This will require a written petition and verifiable documentation. Petition forms are available for undergraduate students in the CLAS advising office and from the Graduate School for graduate students. The signature of a faculty member on a SAF does not guarantee that a late add petition will be approved.
o  Late drops/withdrawals (after 20 April) will be approved only when circumstances surrounding the late drop have arisen after the published drop deadline and are beyond the student’s control. This will require a written petition and verifiable documentation. The signature of a faculty member does not guarantee that a late drop/withdrawal petition will be approved after April 20. After April 20th, students should meet with their CLAS advisor or Graduate School Coordinator to learn more about how to petition to drop or withdraw from a course late.
·  Tuition: Students are responsible for completing arrangements with financial aid, family, scholarships, etc. to pay their tuition prior to Census Date (4 February). Students who drop after that date are (1) financially responsible for tuition and fees, (2) academically responsible and will receive a "W" grade, and (3) are ineligible for a refund of COF hours or tuition.
·  Graduation:
·  Undergraduate students wishing to graduate in Spring 2015 should (1) first meet with their CLAS advisor; (2) meet with their major and minor advisor(s), who will complete the electronic form required to verify eligibility to graduate; and (3) apply for graduation online through UCD Access. These steps must be completed by no later than 5PM on February 4, 2015, which is an absolute deadline without exception.
·  Graduate students wishing to graduate in Spring 2015 must apply for graduation online through UCDAccess and have a Request for Admissions to Candidacy on file with the CU Denver Graduate School (LSC 1251) no later than 5PM on February 4, 2015, which is an absolute deadline without exception.
Important Dates and Deadlines
·  January 19, 2015: Martin Luther King Holiday. Last day to withdraw from all classes via UCDAccess and receive a refund of all tuition that has been paid.
·  January 20, 2015: First day of classes.
·  January 25, 2015: Last day to add or waitlist classes using UCDAccess without permission. After this date, a CLAS Instructor Permission to Enroll form is required for any late add requests.
·  January 26, 2015: Last day to drop without a $100 drop charge. No adds permitted on this day.
·  January 27 – February 4, 2015:
o  To add a course from January 27-February 4, it is the student's responsibility to get a CLAS Instructor Permission to Enroll form at http://www.ucdenver.edu/academics/colleges/CLAS/clas-advising/Pages/CLASAdvising.aspx, have it signed in person and submit it or route it electronically, according to the instructions on the form. Students and faculty will receive emails with directions for confirming registration via official university email and students must verify their schedules before census, February 4th, by 5p.m. After February 4th, students should meet with their CLAS advisor or Graduate School Coordinator to learn more about how to petition to add a course late.
·  February 4, 2015: Census date.
o  2/4/115, 5 PM: Last day to add structured courses without a written petition for a late add. This is an absolute deadline and is treated as such. This does not apply to independent studies, internships, project hours, thesis hours, dissertation hours, and modular courses, though it is in the student’s best interest to have requested all late adds by this date.
o  2/4/15, 5 PM: Last day to drop a Spring 2015 course or completely withdraw from all courses using the UCD Access Portal and still receive a tuition refund, minus the drop fee(s). After this date, tuition is forfeited and a "W" will appear on the transcript. This includes section changes and is an absolute deadline.
o  2/4/15, 5 PM: Last day to request Pass/Fail or No-Credit option for a course using a Schedule Adjustment Form.
o  2/4/15, 5 PM: Last day for a graduate student to register for a Candidate for Degree and last day for a Ph.D. student to petition for a reduction in hours.
o  2/4/15, 5 PM: Last day to apply for Spring 2015 graduation.
o  February 16-25, 2015: Early Alert open to faculty
o  March 23-29, 2015: Spring Break-(no classes; campus open).
o  April 6, 2015, 5 PM: Last day for non-CLAS students to drop or withdraw without a petition and special approval from the academic dean. After this date, a dean’s signature is required.
o  April 20, 2015, 5 PM: Last day for CLAS students to drop or withdraw with signatures from the faculty and dean but without a full petition. After this date, all schedule changes require a full petition.
o  May 11-16, 2015: Finals Week. No schedule changes will be granted once finals week has started--there are no exceptions to this policy. Commencement is May 16.
o  May 21, 2015, 5 PM: Due date for faculty submission of grades.
o  May 24, 2015: Spring final grades available on UCD Access (tentative).