Complexity Theory, Game Theory, and Economics: The Barbados Lectures

TL;DR

This paper presents lecture notes exploring how complexity theory informs economic and game-theoretic barriers and how game theory has spurred advances in complexity theory, with applications to equilibrium computation.

Contribution

It provides an accessible overview of the interplay between complexity, game theory, and economics, highlighting recent breakthroughs and illustrating the mutual influence of these fields.

Findings

Complexity theory sheds light on barriers in economics and game theory.

Game-theoretic questions have driven new developments in complexity theory.

Recent breakthroughs connect equilibrium computation with complexity classes.

Abstract

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.