TUTORIAL: Computational Game Theory

 

 

Recently there has been renewed interest in game theory in several research disciplines, with its uses ranging from the modeling of evolution to the design of distributed protocols. In the AI community, game theory is emerging as the dominant formalism for studying strategic and cooperative interaction in multi-agent systems.

 

Classical work provides rich mathematical foundations and equilibrium concepts, but relatively little in the way of computational and representational insights that would allow game theory to scale up to large, complex systems. The rapidly emerging field of computational game theory is addressing such algorithmic issues, and this tutorial will provide a survey of developments. Special emphasis will be placed on the interdisciplinary flavor of the field, drawing on methods and insights from artificial intelligence, machine learning, theoretical computer science, economics, biology, and many other fields.

 

Among the topics to be covered are:

 

§         Examples of Strategic Conflict as Matrix Games

§         Basics Definitions of (Matrix) Game Theory

§         Notions of Equilibrium: Overview

§         Definition and Existence of Nash Equilibria

§         Computing Nash Equilibria for Matrix Games

§         Graphical Models for Multiplayer Game Theory

§         Computing Nash Equilibria in Graphical Games

§         Probabilistic Inference and Game Theory

§         Bayesian Networks and Graphical Games

§         Sampling Methods in Game Theory

§         Congestion Games and Summarization Games

§         Social Network Theory and Computational Game Theory

§         Interdependent Security and Game Theory

§         Other Equilibrium Concepts:

o        Correlated Equilibria,

o        Correlated Equilibria and Graphical Games,

o        Evolutionary Stable Strategies,

o        Nash's Bargaining Problem, Cooperative Equilibria

§         Learning in Repeated Games:

o        Classical Approaches,

o        Regret Minimizing Algorithms,

o        Connections to Machine Learning

§         Games with State:

o        Connections to Reinforcement Learning

§         Other Directions and Conclusions

 

The tutorial will be self-contained, assuming no prior knowledge of game theory.

 

Biosketch of the presenter:

Michael Kearns is Professor of Computer and Information Science the University of Pennsylvania, where he is also co-director of Penn's Institute for Research in Cognitive Science. Prior to joining Penn, he spent a decade in basic research at AT&T/Bell Labs, where he led the machine learning and artificial intelligence research group. Kearns has published extensively in artificial intelligence, machine learning, theoretical computer science, computational game theory, and related fields. He is the author of "An Introduction to Computational Learning Theory" (with U. Vazirani; MIT Press, 1994). He received his undergraduate education at U.C. Berkeley in math and computer science, and a Ph.D. in computer science from Harvard University. For more information, please visit www.cis.upenn.edu/~mkearns.