Game Theory II: Advanced Applications

About this course: Popularized by movies such as "A Beautiful Mind", game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Over four weeks of lectures, this advanced course considers how to design interactions between agents in order to achieve good social outcomes. Three main topics are covered: social choice theory (i.e., collective decision making and voting systems), mechanism design, and auctions. In the first week we consider the problem of aggregating different agents' preferences, discussing voting rules and the challenges faced in collective decision making. We present some of the most important theoretical results in the area: notably, Arrow's Theorem, which proves that there is no "perfect" voting system, and also the Gibbard-Satterthwaite and Muller-Satterthwaite Theorems. We move on to consider the problem of making collective decisions when agents are self interested and can strategically misreport their preferences. We explain "mechanism design" -- a broad framework for designing interactions between self-interested agents -- and give some key theoretical results. Our third week focuses on the problem of designing mechanisms to maximize aggregate happiness across agents, and presents the powerful family of Vickrey-Clarke-Groves mechanisms. The course wraps up with a fourth week that considers the problem of allocating scarce resources among self-interested agents, and that provides an introduction to auction theory. You can find a full syllabus and description of the course here: http://web.stanford.edu/~jacksonm/GTOC-II-Syllabus.html There is also a predecessor course to this one, for those who want to learn or remind themselves of the basic concepts of game theory: https://www.coursera.org/learn/game-theory-1 An intro video can be found here: http://web.stanford.edu/~jacksonm/Game-Theory-2-Intro.mp4

Who is this class for: This course is based on advanced undergraduate and masters level material and is aimed at researchers, students, and practitioners who wish to learn more about game theory and mechanism design. This course is a follow up to our first Game Theory course, and it presumes that the students are comfortable with the material from that course. You must be also comfortable with mathematical thinking and rigorous arguments. Relatively little specific math is required; however the course involves some probability theory (for example, you should know what a conditional probability is) and some calculus.

Created by:  Stanford University, The University of British Columbia

• Taught by:  Matthew O. Jackson, Professor

  Economics

• Taught by:  Kevin Leyton-Brown, Professor

  Computer Science

• Taught by:  Yoav Shoham, Professor

  Computer Science

Level Advanced Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.7 stars Average User Rating 4.7See what learners said Coursework

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Stanford University The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto, California, United States. The University of British Columbia The University of British Columbia is a global centre for research and teaching.

Syllabus


WEEK 1


Social Choice
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8 videos, 1 reading, 3 practice quizzes expand

1. Video: An Introduction to the Course
2. Reading: Syllabus
3. Video: 1.1 Social Choice: Taste
4. Video: 1.2 Social Choice: Voting Scheme
5. Video: 1.3 Paradoxical Outcomes
6. Video: 1.4 Impossibility of Non-Paradoxical Social Welfare Functions
7. Video: 1.5 Arrow's Theorem
8. Video: 1.6 Impossibility of Non-Pardoxical Social Choice Functions
9. Video: 1.7 Single-Peaked Preferences
10. Practice Quiz: Unit 1.2 Quiz
11. Practice Quiz: Unit 1.3 Quiz
12. Practice Quiz: Unit 1.5 Quiz

Graded: Problem Set 1

WEEK 2


Mechanism Design
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9 videos, 1 reading, 5 practice quizzes expand

1. Video: 2.1 Mechanism Design: Taste
2. Video: 2.2 Implementation
3. Video: 2.3 Mechanism Design: Examples
4. Video: 2.4 Revelation Principle
5. Video: 2.5 Revelation Principle: Examples
6. Video: 2.6 Impossibility of General Dominant-Strategy Implementation
7. Video: 2.7 Transferable Utility
8. Video: 2.8 Transferable Utility Example
9. Video: 2.9 Mechanism Design as an Optimization Problem
10. Practice Quiz: Unit 2.2 Quiz
11. Practice Quiz: Unit 2.4 Quiz
12. Practice Quiz: Unit 2.6 Quiz
13. Practice Quiz: Unit 2.8 Quiz
14. Practice Quiz: Unit 2.9 Quiz
15. Reading: Reading on the theory of Mechanism Design

Graded: Problem Set 2

WEEK 3


Efficient Mechanisms
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6 videos, 3 practice quizzes expand

1. Video: 3.1 VCG: Taste
2. Video: 3.2 VCG: Definitions
3. Video: 3.3 VCG: Examples
4. Video: 3.4 VCG: Limitations
5. Video: 3.5 VCG: Individual Rationality and Budget Balance in VCG
6. Video: 3.6 VCG: The Myerson-Satterthwaite Theorem
7. Practice Quiz: Unit 3.2 Quiz
8. Practice Quiz: Unit 3.3 Quiz
9. Practice Quiz: Unit 3.6 Quiz

Graded: Problem Set 3

WEEK 4


Auctions
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7 videos, 4 practice quizzes expand

1. Video: 4.1 Auctions: Taste
2. Video: 4.2 Auctions: Taxonomy
3. Video: 4.3 Bidding in Second-Price Auctions
4. Video: 4.4 Bidding in First-Price Auctions
5. Video: 4.5 Revenue Equivalence
6. Video: 4.6 Optimal Auctions
7. Video: 4.7 Advanced Auctions
8. Practice Quiz: Unit 4.2 Quiz
9. Practice Quiz: Unit 4.3 Quiz
10. Practice Quiz: Unit 4.4 Quiz
11. Practice Quiz: Unit 4.6 Quiz

Graded: Problem Set 4

WEEK 5


Final Exam
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Graded: FINAL EXAM