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Complexity Theory, Game Theory, and Economics: The Barbados Lectures
This document collects the lecture notes from my mini-course "Complexity
Theory, Game Theory, and Economics," taught at the Bellairs Research Institute
of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th
McGill Invitational Workshop on Computational Complexity.
The goal of this mini-course is twofold: (i) to explain how complexity theory
has helped illuminate several barriers in economics and game theory; and (ii)
to illustrate how game-theoretic questions have led to new and interesting
complexity theory, including recent several breakthroughs. It consists of two
five-lecture sequences: the Solar Lectures, focusing on the communication and
computational complexity of computing equilibria; and the Lunar Lectures,
focusing on applications of complexity theory in game theory and economics. No
background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some
recent citations to v1 Revised v3 corrects a few typos in v
An Investigation Report on Auction Mechanism Design
Auctions are markets with strict regulations governing the information
available to traders in the market and the possible actions they can take.
Since well designed auctions achieve desirable economic outcomes, they have
been widely used in solving real-world optimization problems, and in
structuring stock or futures exchanges. Auctions also provide a very valuable
testing-ground for economic theory, and they play an important role in
computer-based control systems.
Auction mechanism design aims to manipulate the rules of an auction in order
to achieve specific goals. Economists traditionally use mathematical methods,
mainly game theory, to analyze auctions and design new auction forms. However,
due to the high complexity of auctions, the mathematical models are typically
simplified to obtain results, and this makes it difficult to apply results
derived from such models to market environments in the real world. As a result,
researchers are turning to empirical approaches.
This report aims to survey the theoretical and empirical approaches to
designing auction mechanisms and trading strategies with more weights on
empirical ones, and build the foundation for further research in the field
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