Dr Paul Duetting Columbia House COL 3.08

This course is available on the MSc in Applicable Mathematics and MSc in Operations Research & Analytics. This course is available with permission as an outside option to students on other programmes where regulations permit.

Students must have completed Algorithms and Computation (MA407) or have taken an equivalent course that provides basic knowledge in the analysis of algorithms. No prior knowledge about Game Theory is required. 

The last 15-20 years have witnessed a lively interaction between computer science and economics. Many problems central to computer science – from resource allocation problems in large networks to online advertising – fundamentally involve the interaction of multiple self-interested parties. Game theory and mechanism design offer a host of models and definitions to reason about such problems. But the flow of ideas also travels in the opposite direction, as research in computer science has complemented the traditional economics literature in several ways. For example, computer science offers a focus on and a language to discuss computational complexity, has popularised the use of approximation guarantees in situations where exact solutions are unrealistic or unknowable, and proposes several alternatives to Bayesian- or average-case analysis that emphasise robust solutions to economic design problems.

This course gives an overview over the key ideas and developments of this young research field. The focus is on the various new techniques and methods that have been developed, and the new insights that they yield.

Topics covered:

• Complexity of equilibria: hardness of computing pure Nash equilibria, poly-time algorithm for correlated equilibria
• Best response dynamics and no-regret learning: existence and speed of convergence
• Tools for bounding the inefficiency of equilibria: price of anarchy, price of stability, the smoothness framework
• Algorithmic mechanism design: the VCG mechanism and its computational complexity, characterization of truthful mechanisms and techniques for obtaining truthful poly-time approximation mechanisms
• Tools for the design and analysis of simple, robust, non-truthful mechanisms
• Posted price mechanisms and prophet inequalities

This course is delivered through a combination of classes and lectures totaling a minimum of 30 hours across Lent Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.

Students will be expected to produce 10 problem sets in the LT.

Written answers to set problems will be expected on a weekly basis.

1. Noam Nisan, Tim Roughgarden, Eva Tardos, Vijaj V. Vazirani. Algorithmic Game Theory. Cambridge University Press. September 2007.
2. Tim Roughgarden. Twenty Lectures on Algorithmic Game Theory. Cambridge University Press. August 2016.
3. David C. Parkes and Sven Seuken. Introduction to Economics and Computation: A Design Approach. Cambridge University Press. June 2019.

Exam (100%, duration: 2 hours) in the summer exam period.