Math 4390/5390 Game Theory
Summer 2014
Instructor: Burt Simon
Office: CU Building, Room 612
Office Hours: MW before class
Course dates/times: MW 4:00-6:30
Course location: Business 3007
Email: burt.simon@ucdenver.edu
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 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
Official: Math 2421, 3191, and 3800 or 4810
Suggested: Math 3200 and some programming experience
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) all the 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 thoughts 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 so if
you want a single book to read and keep, I suggest that one. 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 Textbook: Game Theory Evolving, 2nd ed., by Herbert Gintis (2009)
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
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Present basic models of conflict and cooperation.
Present solution techniques for simple games based on models of rational play.
Present models of the evolution of game strategies in non-rational agents.
Present applications of the theory in economics, political 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 due at the beginning of class on Monday. We will discuss
homework problems during class when they are due, so sets turned in late cannot receive full
credit.
 There will be a midterm exam and a final exam. Both will be traditional in-class tests.
 Your grade will be based on Homework (at least 25%), Exams (at least 50%), and intangibles like
class participation and work in addition to what is assigned (up to 25%).
Tentative Course Schedule
Class dates
Material Covered
June 9, 11
Introductory examples, Utility theory
References: Gintis, Chapters 2 (advanced) and 3;
Idiot’s Guide, Chapter 18; Davis, Chapter 4
June 16, 18
Two-person zero-sum games
Minimax Theorem, examples
References: Davis, Chapters 2, 3; Idiot’s Guide, Chapter 3
June 23, 25
Solving Zero-Sum games by Linear Programming
Non-zero-sum games, Nash equilibrium (pure, mixed)
References: Gintis, Chapters 4, 5, 6; Davis, Chapter 5;
Idiot’s Guide, Chapters 4, 5
June 30, July 2
Catch-up, and Review
Midterm Exam (2nd half of Wednesday class)
July 7, 9
N-person games, Models of “fairness”
Von Neumann Morgenstern Solutions
Cooperative games, Shapley value, Kernel
References: Rapoport, Chapters 4-7;
Idiot’s Guide, Chapters 9-12
July 14, 16
Repeated Games, Evolutionary Stable Strategy (ESS)
References: Gintis, Chapters 9. 10
Idiot’s Guide, Chapters 17 and 22
July 21, 23
Population Dynamics and Evolutionary Game Theory
References: Gintis, Chapters 11, 12
July 28, Aug 30,
Catch-up, Review, and Final Exam