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# Game Theory

## Course Syllabus

Week 1. Introduction: Introduction, overview, uses of game theory, some applications and examples, and formal definitions of: the normal form, payoffs, strategies, pure strategy Nash equilibrium, dominated strategies.

Week 2. Mixed-strategy Nash equilibria: Definitions, examples, real-world evidence.

Week 3. Alternate solution concepts: iterative removal of strictly dominated strategies, minimax strategies and the minimax theorem for zero-sum game, correlated equilibria.

Week 4. Extensive-form games: Perfect information games: trees, players assigned to nodes, payoffs, backward Induction, subgame perfect equilibrium, introduction to imperfect-information games, mixed versus behavioral strategies.

Week 5. Repeated games: Repeated prisoners dilemma, finite and infinite repeated games, limited-average versus future-discounted reward, folk theorems, stochastic games and learning.

Week 6. Coalitional games: Transferable utility cooperative games, Shapley value, Core, applications.

Week 7. Bayesian games: General definitions, ex ante/interim Bayesian Nash equilibrium.

## Recommended Background

## Suggested Readings

- Essentials of Game Theory, by Kevin Leyton-Brown and Yoav Shoham; Morgan and Claypool Publishers, 2008. This book has the same structure as the course, and covers most of the same material. It is free if you access the link from a school that subscribes to the Morgan & Claypool Synthesis Lectures, and otherwise costs $5 to download. You can also get it as a printed book from (e.g.) amazon.com, or as an ebook for Kindle or Google devices.
- A Brief Introduction to the Basics of Game Theory, by Matthew O. Jackson. These notes offer a quick introduction to the basics of game theory; they are available as a free PDF download.

## Course Format

The course consists of the following materials:

- Videos. The lectures are delivered via videos, which are broken into small chunks, usually between five and fifteen minutes each. There will be approximately one and a half hours of video content per week. You may watch the lecture videos at your convenience. Lower-resolution videos are also available for those with slow internet connections.
- Slides. We have made available pdf files of all the lecture slides.
- Quizzes. There will be non-graded short "quiz" questions that will follow some of the videos to help you gauge your understanding.
- Online Lab Exercises After some of the videos, we will ask you to go online to play some games. These are entirely optional, and are designed to illustrate some of the concepts from the course.
- Problem Sets. There will also be graded weekly problem sets that you will also answer online, but may work through offline; those must be completed within two weeks of the time that they are posted in order to be graded for full credit. If you miss a problem set deadline, you may complete it before the end of the course for half credit. You may discuss problems from the problem sets with other students in an online forum, without providing explicit answers.
- Final Exam. There will be an online final exam that you will have to complete within two weeks of its posting. Once you begin the exam, you will have four hours to complete it.
- Screen-side Chats. A couple of times during the course, we will hold a brief online chat where we answer questions and discuss topics relevant to the course.

## FAQ

**Will I get a statement of accomplishment after completing this class?**Yes. Students who successfully complete the class will receive a statement of accomplishment signed by the instructors.

## Instructor(s)

## Matthew O. Jackson

### William D. Eberle Professor of Economics, Stanford University

Matthew O. Jackson is the William D. Eberle Professor of Economics at Stanford University and an external faculty member of the Santa Fe Institute and a fellow of CIFAR. Jackson's research interests include game theory, microeconomic theory, and the study of social and economic networks, on which he has published many articles and the book Social and Economic Networks.

## Yoav Shoham

### Professor of Computer Science, Stanford University

Yoav Shoham received his PhD in computer science from Yale University in 1987, and has been a Professor of Computer Science at Stanford University since then. His research interests include logic-based knowledge representation, game theory, and electronic commerce. He has published numerous articles in these areas, and five books. The last one, Essentials of Game Theory (co-written with K. Leyton-Brown), covers the material in this course. Prof. Shoham has also founded several successful internet companies.

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