GVPT 399A - SPRING 2003

THE MATEMATICS OF HUMAN BEHAVIOR

Instructor:          Professor Piotr Swistak, TYD 1135 B, tel. 405-4149

Email: pswistak@gvpt.umd.edu.

Office hours:      Mondays 11:00-12:00 or by appointment.

Lectures:            TYD 1108, Tuesdays 3:30-6:15 pm.

This is an introductory in game theory.  Game theory is a general theory of rational behavior.  While it has long been used by all social sciences, its impact of the last two decades has been extraordinary and unprecedented. My plan is to give you a brief, yet reasonably comprehensive overview of modern game theory.  We will cover theory of preferences (ordinal utility), expected utility theory, and a variety of solutions concepts including iterated dominance, Nash equilibria, subgame perfect equilibria, rationalizable strategies and equilibria in beliefs and evolutionary equilibria. 

BOOKS

Avinash Dixit and Susan Skeath, Games of Strategy, Norton, 1999.

Robert Axelrod, The Evolution of Cooperation, Basic Books, 1984.

WARNING

Material in this course is both extensive and challenging.  As the title of the course suggests, much of the material will be mathematical¾students who are not perfectly comfortable with basic mathematics/simple algebra will not be able to continue in this class.

GRADING

There will be weekly homeworks, several short tests (testing your understanding of the material covered) and an optional final exam.  Tests will be announced about a week ahead of time.  I will propose your course grade on the basis of tests (70% of the grade) and homeworks (30%).  In class group projects/competitions will be the only source of an extra credit.

If you choose to take the final exam, it will give you an additional opportunity to improve your grade.  The final will count 30%. 

Finally, I reserve the right to take into consideration any additional information that would indicate the amount of effort you have invested in this class.  This includes attendance and class participation (as measured by in-class group exercises.)

While all testing is closed book, your are allowed to have a crib sheet─a single standard size sheet of paper with whatever information you want to put on it.

Make-up tests will not be allowed except for special, well documented cases like medical emergencies.  You have to inform me about such emergencies immediately.  I will also ask you to supply official documents (from the physician, hospital, etc).  If you neglect to inform me in a reasonable time, I will assign zero points to all missed tests; there will be no appeals.

Lectures are meant to supplement the readings.  A good part of the material will not be contained in the readings and will only be presented in class.  Attending classes will hence be necessary to do well in this course. There are no other ways to get extra credit.

SPECIAL PROBLEMS AND SITUATIONS

If you have any problems, e.g., medical, that can affect your performance in class you should let me know immediately.  We may be able to resolve the problem if you come and tell me about it in advance.

TENTATIVE SCHEDULE OF READINGS

Readings below are labeled by the “weeks” in which the relevant material will be covered.  (For the corresponding calendar dates which define each week see THE CALENDAR below.) 

WEEK 1

                             Introduction: Examples of Topics, Methods, and Solutions

For next class please read Dixit and Skeath, Appendix: Probability and Expected Utility (pp. 163-177.)

WEEK 2

Choice under Certainty: Theory of Preferences

For next class please read Dixit and Skeath Chapter1.

WEEK 3

Choice under Uncertainty: Von Neumann-Morgenstern Expected Utility Theory and the Foundation of Game Theory

For next class please read Dixit and Skeath Chapter 2.

WEEK 4

Game Theory: Primitive Terms, their Properties and Interpretations

For next class please read Dixit and Skeath Chapter 3.

WEEK 5

Sequential Games and Rollback Equilibria

For next class please read Dixit and Skeath Chapter 4.

WEEK 6

Simultaneous-Move Games: Dominance Solvability and Nash Equilibria

For next class please read Dixit and Skeath Chapter 5.

WEEK 7

Simultaneous-Move Games: Mixed Strategies, Zero-Sum Games, Minimax

For next class please read Dixit and Skeath Chapters 6 (Chapter 7 is also recommended).

WEEK 8

Sequential versus Simultaneous-Move Games and Subgame-Perfect Equilibria

For next class please read Dixit and Skeath Chapter 8.

WEEKS 9 & 10

NO CLASS

WEEK 11

                                                Repeated Games and Folk Theorem

For next class please read Dixit and Skeath Chapter 10 section 1 and 2.

WEEK 12

Evolutionary Games

For next class please read Axelrod Part I and II.

WEEK 13

The Evolutionarily Stable Strategies and the Evolution of Cooperation   

For next class please read Axelrod Part III, IV and V.

WEEK 14

The Evolution of Social Structure

For next class please read Bendor and Swistak (1997).

WEEK 15

The Evolution of Social Structure (continued)

For next class please read Bendor and Swistak (2001).

WEEK 16

REVIEW

THE CALENDAR

Week 1  (January 28)

Week 2  (February 4)

Week 3  (February 11)

Week 4  (February 18)

Week 5  (February 25)

Week 6  (March 4)

Week 7  (March 11)      

Week 8  (March 18)                  

Week 9  (March 25)   SPRING BREAK   

Week 10  (April 1)     NO CLASS

Week 11  (April 8)

Week 12  (April 15)       

Week 13  (April 22)       

Week 14 (April 29)

Week 15 (May 6)

Week 16 (May 12)