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Game Theory II: Advanced Applications

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  • Certificate

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.

 

Faculty

Matthew O. Jackson
Professor
Yoav Shoham
Professor

*Program faculty is subject to change

Curriculum

WEEK 1: 4 hours to complete

Social Choice

  • 8 videos
    • An Introduction to the Course9m
    • 1.1 Social Choice: Taste 3m
    • 1.2 Social Choice: Voting Scheme 15m
    • 1.3 Paradoxical Outcomes 9m
    • 1.4 Impossibility of Non-Paradoxical Social Welfare Functions 5m
    • 1.5 Arrow's Theorem 31m
    • 1.6 Impossibility of Non-Pardoxical Social Choice Functions 7m
    • 1.7 Single-Peaked Preferences 7m
  • 1 reading
    • Syllabus10m
  • 4 practice exercises
    • Problem Set 130m
    • Unit 1.2 Quiz30m
    • Unit 1.3 Quiz30m
    • Unit 1.5 Quiz30m

WEEK 2: 5 hours to complete

Mechanism Design

  • 9 videos
    • 2.1 Mechanism Design: Taste 3m
    • 2.2 Implementation 18m
    • 2.3 Mechanism Design: Examples12m
    • 2.4 Revelation Principle 9m
    • 2.5 Revelation Principle: Examples5m
    • 2.6 Impossibility of General Dominant-Strategy Implementation 11m
    • 2.7 Transferable Utility 9m
    • 2.8 Transferable Utility Example8m
    • 2.9 Mechanism Design as an Optimization Problem 19m
  • 1 reading
    • Reading on the theory of Mechanism Design10m
    • Unit 2.2 Quiz30m
    • Unit 2.4 Quiz30m
    • Unit 2.6 Quiz30m
    • Unit 2.8 Quiz30m
    • Unit 2.9 Quiz30m

WEEK 3: 3 hours to complete

Efficient Mechanisms

  • 6 videos
    • 3.1 VCG: Taste 10m
    • 3.2 VCG: Definitions 18m
    • 3.3 VCG: Examples 7m
    • 3.4 VCG: Limitations 11m
    • 3.5 VCG: Individual Rationality and Budget Balance in VCG 16m
    • 3.6 VCG: The Myerson-Satterthwaite Theorem 19m
  • 4 practice exercises
    • Problem Set 330m
    • Unit 3.2 Quiz30m
    • Unit 3.3 Quiz30m
    • Unit 3.6 Quiz30m

WEEK 4: 4 hours to complete

Auctions

  • 7 videos
    • 4.1 Auctions: Taste 3m
    • 4.2 Auctions: Taxonomy 14m
    • 4.3 Bidding in Second-Price Auctions 6m
    • 4.4 Bidding in First-Price Auctions 13m
    • 4.5 Revenue Equivalence 40m
    • 4.6 Optimal Auctions 21m
    • 4.7 More Advanced Auctions 12m
  • 5 practice exercises
    • Problem Set 430m
    • Unit 4.2 Quiz30m
    • Unit 4.3 Quiz30m
    • Unit 4.4 Quiz30m
    • Unit 4.6 Quiz30m

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