Popularised 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), mechanism design, and auctions.
In the first week the course 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. The course considers the problem of making collective decisions when agents are self interested and can strategically misreport their preferences. The course explains "mechanism design" a broad framework for designing interactions between self-interested agents and give some key theoretical results.
There will be four weeks of materials consisting of online videos and problem sets. the course recommends that the candidate should complete the problem set for each week within that week, although the hard deadline is two weeks from the release date. On the fifth week, the candidate will have a final exam.
Week 1. Social Choice
Week 2. Mechanism Design
Week 3. Efficient Mechanisms
Week 4. Auctions
Week 5-6. Final exam and final problem set.
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