Algorithmic Game Theory, Mechanism Design and Computational Economics

Advanced Course, 2+1

Basic Information

Lecturer: Yun Kuen Cheung (You may call me Marco.)
Lectures: Monday 4pm to 6pm, Room 021 in Building E1.4
Tutor: Bhaskar Ray Chaudhury
Tutorials: Alternating Tuesday 2pm to 4pm, Room 021 in Building E1.4
Credits: 5
Prerequisites: The following knowledge is assumed from enrolled students:
  • Basic knowledge in algorithms and data structure, and their analyses
  • Calculus, including the concepts of limit, convergence, derivative and integration
The following knowledge will be useful in some parts of the course, but NOT a prerequisite for enrolling:
  • Basics of probability theory (what are discrete/continuous distributions, expected values and variances)
  • Linear programming and its duality
  • Basic max-flow algorithm, e.g. Ford-Fulkerson
 

 

Description

(Currently, we are giving a brief desciption to facilitate students' planning. We will update this decription with more details later.)

Games and markets arise wherever there are two or more agents competing for selfish benefits. In their enormous applications, "agents" can refer to humans, animals, computers, bacterias or even molecules.

In the past 20 years, the algorithmic/computational aspects of game/market/auction theory have grown to become a popular topic in (theoretical) computer science, economics, operational research, dynamical system, and more. In this course, we will discuss the very core of this exciting new research direction.

For ambitious students who want to develop rigorous theoretical training related to this topic, I can suggest extra materials for reading and thinking.

This course is divided into three parts.

In the first part, we cover some basic concepts in games and markets, including Zero-sum Game and General-sum Game, Nash EquilibriumMarket Equilibrium, Correlated Equilibrium and Regret Minimization. Algorithms for finding such equilibria in will be presented.

Concerning equilibrium, one fundamental question is how good an equilibrium is. Prisoner Dilemma is a canonical example to show that Nash Equilibrium can be very bad. Efficiency measures and techniques, e.g. Price of Anarchy and Smoothness, will be covered.

In the second part, we address another fundamental question concerning equilibrium: how an equilibrium is reached. We will introduce and study a number of simple game/market dynamics, e.g. Tatonnement and Proportional Response Dynamic, aiming to explain how equilibrium can be reached in a highly distributed environment, in which individual agents can access very limited local information only. We will also look into an interesting special case of Linear Fisher/Exchange market, for which non-trivial flow-type algorithms are developed.

In the third part, we focus on the prominent application of game theory in the digital era --- design of auction, or what we call the Mechanism Design, e.g. eBay, Google ad auction, spectrum auction. In the simplest setting, there is an auctioneer selling a number of items, and there are many agents who are interested in those items. Mechanism design concerns

  • the design of communication protocols between auctioneer and agents
  • design of efficient (poly-time, or even stricter time requirement due to practical applications) algorithms to decide the allocation of items which achieve good efficiency
  • design of truthful mechanism which motivates agents not to be strategic on reporting their preferences

Online Reference

Our course will have some overlaps with the following materials. We will also provide self-contained lecture notes in this webpage.