Essentials of game theory

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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.

"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

"I wish I'd had a comprehensive, clear and rigorous introduction to the essentials of game theory in under one hundred pages when I was starting out." --David Parkes, Harvard University, Computer Science

"Beside being concise and rigorous, Essentials of Game Theory 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

"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

"Although written by computer scientists, this book serves as a sophisticated introduction to the main concepts and results of game theory from which other scientists, including social scientists, can greatly benefit. In eighty pages, Essentials of Game Theory formally defines key concepts, illustrated with apt examples, in both cooperative and noncooperative game theory." --Steven Brams, New York University, Political Science

"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

"To a large extent, modern behavioral ecology and behavioral economics are studied in the framework of game theory. Students and faculty alike will find this concise, rigorous and clear introduction to the main ideas in game theory immensely valuable." --Marcus Feldman, Stanford University, Biology

"This unique book is today 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

"Excerpted from a much-anticipated, cross-disciplinary book on multiagent systems, this terse, incisive and transparent book is the ideal introduction to the key concepts and methods of game theory for researchers in several fields, including artificial intelligence, networking, and algorithms." --Vijay Vazirani, Georgia Institute of Technology, Computer Science

"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

Author(s): Kevin Leyton-Brown
Series: Synthesis Lectures on Artificial Intelligence and Machine Learning
Edition: 1
Publisher: Morgan and Claypool Publishers
Year: 2008

Language: English
Pages: 104

GTessentials.pdf......Page 0
Games in Normal Form......Page 17
Example: the TCP user's game......Page 18
Prisoner's Dilemma......Page 19
Common-payoff Games......Page 20
Zero-sum Games......Page 21
Strategies in normal-form games......Page 22
Pareto optimality......Page 25
Defining best response and Nash equilibrium......Page 26
Finding Nash equilibria......Page 27
Maxmin and minmax strategies......Page 31
Minimax regret......Page 34
Removal of dominated strategies......Page 36
Rationalizability......Page 39
Correlated equilibrium......Page 40
Trembling-hand perfect equilibrium......Page 42
-Nash equilibrium......Page 43
Evolutionarily stable strategies......Page 44
Definition......Page 47
Strategies and Equilibria......Page 48
Subgame-perfect equilibrium......Page 51
Backward induction......Page 54
Definition......Page 57
Strategies and equilibria......Page 58
Sequential equilibrium......Page 61
Finitely Repeated Games......Page 65
Infinitely Repeated Games......Page 66
Definition......Page 69
Strategies and Equilibria......Page 70
Uncertainty About Payoffs: Bayesian Games......Page 72
Information Sets......Page 75
Extensive form with Chance Moves......Page 76
Strategies and Equilibria......Page 77
Computing Equilibria......Page 80
EX POST EQUILIBRIA......Page 83
Coalitional games with transferable utility......Page 85
Classes of coalitional games......Page 86
Analyzing Coalitional Games......Page 88
The Shapley Value......Page 89
The Core......Page 91
History and References......Page 93