Game theory is the mathematical study of interaction among independent, self-interested agents. The audience for game theory has grown dramatically in recent years, and now spans disciplines as diverse as political science, biology, psychology, economics, linguistics, sociology, and computer science, among others. What has been missing is a relatively short introduction to the field covering the common basis that anyone with a professional interest in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This Synthesis Lecture aims to fill this gap by providing a concise and accessible introduction to the field. It covers the main classes of games, their representations, and the main concepts used to analyze them.
High Praise for Essentials of Game Theory
“Best short introduction to game theory I have seen! I wish it was available when I started being interested in the field!” – Silvio Micali, MIT, Computer Science
“This introduction is just what a growing multidisciplinary audience needs: it is concise, authoritative, up to date, and clear on the important conceptual issues.” – Robert Stalnaker, MIT, Linguistics and Philosophy
“Beside being concise and rigorous it is also quite comprehensive. It includes the formulations used in most applications in engineering and the social sciences, and illustrates the concepts with relevant examples.”
– Robert Wilson, Stanford University, Graduate School of Business
“This unique book is the best short technical introduction to game theory. Accessible to a broad audience, it will prove invaluable in artificial intelligence, more generally in computer science, and indeed beyond.”
– Moshe Tennenholtz, Technion, Industrial Engineering and Management
“The authors admirably achieve their aim of providing a scientist or engineer with the essentials of game theory in a text that is rigorous, readable and concise.”
– Frank Kelly, University of Cambridge, Statistical Laboratory
“This book will appeal to readers who do not necessarily hail from economics, and who want a quick grasp of the fascinating field of game theory. The main categories of games are introduced in a lucid way and the relevant concepts are clearly defined, with the underlying intuitions always provided.”
– Krzysztof Apt, University of Amsterdam – Institute for Logic, Language and Computation
Table of Contents
Games in Normal Form
Analyzing Games: From Optimality to Equilibrium
Further Solution Concepts for Normal-Form Games
Games with Sequential Actions: The Perfect-information Extensive Form
Generalizing the Extensive Form: Imperfect-Information Games
Repeated and Stochastic Games
Uncertainty about Payoffs: Bayesian Games
Coalitional Game Theory
History and References
About the Author(s)
Kevin Leyton-Brown, University of British Columbia
Kevin Leyton-Brown is a professor of Computer Science at the University of British Columbia and an associate member of the Vancouver School of Economics. He holds a PhD and M.Sc. from Stanford University (2003; 2001) and a B.Sc. from McMaster University (1998). He studies the intersection of computer science and microeconomics, addressing computational problems in economic contexts and incentive issues in multiagent systems. He also applies machine learning to the automated design and analysis of algorithms for solving hard computational problems.
Yoav Shoham, Stanford University
Yoav Shoham is Professor of Computer Science at Stanford University, where he has been since receiving his PhD in Computer Science from Yale University in 1987 and spending an abbreviated post-doctoral position at the Weizmann Institute of Science. He has worked in various areas of AI, including temporal reasoning, nonmonotonic logics and theories of commonsense. Shoham’s interest in recent years has been multiagent systems, and in particular the interaction between computer science and game theory. Shoham is a Fellow of the Association for Advancement of Artificial Intelligence (AAAI), and charter member of the Game Theory Society. He is an author of four books, an editor of one, and an author of numerous articles. He is also a founder of several successful e-commerce software companies.
Beyond its obvious attractiveness, game theory is one of the fundamental techniques in decision systems. Its development spans almost a century and is still an open avenue of research. However, since it’s crowded with mathematical difficulties that make the methods cumbersome to read and apply, most newcomers to the field find it very difficult to understand. This is not true, though, as this short book nicely shows. As Leyton-Brown and Shoham notice in the preface, it is rather difficult to imagine that anyone who wishes to enter the field of game theory is unaware of many, if not all, of the concepts discussed in the text. Therefore, this is a book with a concise, clear, and organized introduction to the main concepts of game theory. For the ambitious reader, the book often discusses current scientific research. In other words, it is a gentle introduction, covering the basics of game theory to the current state of the art, in easy-to-read and understandable language.
The book is very well organized. The chapters follow one another naturally and, surprisingly, the level of difficulty is kept the same throughout the book–compared to other technical books where the difficulty increases as reading progresses. It also does an excellent service of providing a wonderful motivation for the study of game theory, without getting into very involved discussions on rationality and other related concepts that often appear in other books on game theory. The book covers the main topics–representational issues and different sorts of equilibria computing–with clarifying examples. The book does not end every chapter with a collection of exercises, but the alert reader will find, scattered throughout the book, key questions that better serve this purpose. It also doesn’t end each chapter with a proper discussion of historical remarks, but the expositions are often complemented with annotations of who did what and why. Also, although the book does not provide chapter cross-referencing in the beginning, all chapters in the book have plenty of pointers to other sections that make it easy to read them in a different order and still grasp the main concepts. Despite its small size, this book presents a lot of information about game theory.
Carlos Linares Lopez – ACM Computing Review