Course Objective: The goal of this class is to provide a broad and rigorous introduction to the theory, methods and algorithms of multi-agent systems. The material spans disciplines as diverse as engineering (including control theory and signal processing), computer science (including artificial intelligence, algorithms and distributed systems), micro-economic theory, operations research, public policies, psychology and belief systems. A primary focus of the course is on the application of cooperative and non-cooperative game theory for both static and dynamic models, with deterministic as well as stochastic descriptions. The coverage will encompass both theoretical and algorithmic developments, with multi-disciplinary applications.
Prerequisites:The course is offered as a graduate level course. To follow the course, familiarity with dynamic systems (at the level of ECE-GY 6253), some background in probability theory (at the level of ECE-GY 6303) are desirable. Some familiarity with the basics of linear and nonlinear programming is desirable but not required.
Exams and Homeworks:
- Homework problems will be assigned on a regular basis throughout the semester to be handed in at the beginning of class on the date due. There will be 5-6 homeworks. Solutions to the assigned problems will be provided. No late homeworks will be accepted.
- Weekly reading homeworks will be assigned. The reading homeworks will consist of research papers, book chapters, lecture notes, etc.
- Each student will be given a scribing assignment to summarize the assigned lecture using LaTeX.
- A term project will be assigned, covering topics not included in the main lectures.
- There will be a midterm exam, with time and place to be announced later.
- The midterm exam is closed book.
- The final exam is closed book and in class during the final exam period.
Grading:
Homeworks (including the scribe assignment): 20%
Midterm Exam: 20%
Final Exam: 25%
Term Project: 20%
Oral Exam/Presentation: 15%
Academic Integrity: You should read the School of Engineering’s Code of Conduct:
Required Text:
[BO] T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edition, Classics in Applied Mathematics, SIAM, Philadelphia, 1999
[FT] D. Fudenberg and J. Tirole, Game Theory, MIT Press, 1991.
[MS] M. Maschler and E. Solan, Game Theory, Cambridge University Press, 2013.
Supplementary Text:
[RG] R. Gibbons, Game Theory for Applied Economists, Princeton University Press, 1992.
[FL] D. Fudenberg and D. K. Levine, The Theory of Learning in Games, MIT Press, 1998.
[OW] G. Owen, Game Theory, 4th edition, Academic Press, 2013.
Additional References:
[RI] R. Isaacs, Differential Games, Kruger, NY, 2nd ed., 1975 (First edition: Wiley, NY, 1965).
[VM] J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ, 2nd ed., 1947 (first edition: 1944).
[VB] T. L. Vincent and J. S. Brown, Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics, Cambridge University Press, Cambridge, England, 2005.
[BB] T. Başar and P. Bernhard, H-infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach, 2nd edition, Birkhäuser, Boston, MA, August 1995.
[CBL] N. Cesa-Bianchi and G. Lugosi, Prediction, Learning, and Games, Cambridge University Press, 2006.
[MOJ] M. O. Jackson, Social and Economic Networks, Princeton University Press, 2010.
[OR] M. J. Osborne and A. Rubinstein, A Course in Game Theory,MIT Press, 1994.
[DBP] D. P. Bertsekas, Dynamic Programming and Optimal Control, Athena Scientific; 4th edition, 2007.
[VK] V. Krishna, Auction Theory, Second Edition, Academic Press, 2009.
[VNRT]V. Vazirani, N. Nisan, T. Roughgarden, and E. Tardos, Eva, Algorithmic Game Theory, Cambridge, UK: Cambridge University Press, 2007.
Course Schedule
Lecture 2: Zero-sum games
Lecture 3: Nonzero-sum games
Lecture 4: Computational and Learning Methods
Lecture 5: Extensive-form games
Lecture 6: Multi-stage games
Lecture 7: Lecture Stackelberg games and repeated games
Lecture 8: Continuous-kernel games
Lecture 9: Bayesian games
Lecture 10: Auction theory
Lecture 11: Mechanism design
Lecture 12: Signaling games
Lecture 13: Nash bargaining solutions
Lecture 14: Cooperative games
Term Project Description
For the term project, you have two options:
Option 1: Choose three references (published after 1980) on a topic of your choice, which have a common theme of relevance to the subject matter of this course. Read these three papers, digest their contents, and write a report (to run 15 type-written pages in IEEE double-column style) explaining (in your own words) their contributions. The report should be a critical survey on the contents of the papers as they relate to the common theme and should indicate possible directions for extensions as you see them.
Option 2: Present (in a written report of at least 10 type-written pages in IEEE double-column style) results of some original research (done by you) on any one of the topics covered in class or listed below. Or develop a numerical algorithm-based software package for cooperative or non-cooperative game solutions, again on a topic relevant to the subject matter of the course, and submit a report that explains the package, and illustrates it on a number of numerical examples (solutions to some game problems).
Due Date for the Final Report: Dec. 20, 2019.
Another deadline: By Oct. 11, 2019, you need to submit a proposal of your project indicating (1) the option (between the two options above), and in case of Option 1 your selection of the three references; (2) motivation (why you choose the topic and why the topic is interesting); (3) introduction and summary of the topic (what is the project is about); (4) anticipated objective (what you plan to achieve at the end of the project); (5) proposed methodologies if you choose Option 2 (what are the proposed tasks that you plan to complete); (6) schedule (what is your project timeline); (7) references. The goal of the proposal is to help you organize your research activities.
The reports should be written in the IEEE journal style. You can find IEEE guidelines as follows:
http://www.ieee.org/publications_standards/publications/authors/authors_journals.html