An Introduction to Game Theory Martin J. Osborne

Game-Theoretic Reasoning pervades economic theory and is used widely in other social and behavioral sciences. This book presents the main ideas of game theory and shows how they can be used to understand economic, social, political, and biological phenomena. It assumes no knowledge of economics, political science, or any other social or behavioral science. It emphasizes the ideas behind the theory rather than their mathematical expression and assumes no specific mathematical knowledge beyond that typically taught in U.S. and Canadian high schools. (Chapter 17 reviews the mathematical concepts used in the book). In particular, calculus is not used, except in the appendix of Chapter 9 (Section 9.8) Nevertheless, all concepts are defined precisely, and logical reasoning is used throughout. My aim is to explain the main ideas of game theory as simply as possible while maintaining complete precision; the more comfortable you are with tight logical analysis, the easier you will find the argument. The only way to appreciate the theory is to see it in action, or better still to put it into action. So the book includes a wide variety of illustrations from the social and behavioral sciences, and over 280 exercises. Each topic is presented with the aid of "Examples", which highlight theoretical points, and "Illustrations", which demonstrate how the theory may be used to understand social, economic, political, and biological phenomena. The "Illustrations" introduce no new theoretical points, and any or all of them may be skipped without loss of continuity. The "Illustrations" for the key models of strategic and extensive games are grouped in separate Chapters (3 and 6). The limited dependencies between chapters mean that several routes may be taken through the book: At a minimum, you should study Chapters 2 (Nash Equilibrium: Theory) and 5 (Extensive Games with Perfect Information: Theory). Optionally you may sample some sections of Chapters 3 (Nash Equilibrium: Illustrations) and 6 (Extensive Games with Perfect Information: Illustrations). You may add to this plan any combination of chapters 4 (Mixed Strategy Equilibrium), 9 (Bayesian Games, except section 9.7, which requires Chapter 4), 7 (Extensive Games with Perfect Information: Extensions and Discussion), 8 (Coalitional Games and the Core), and 16 (Bargaining). If you read Chapter 4 (Mixed Strategy Equilibrium), then you may in addition study any combination of the remaining chapters covering strategic games, and if you study Chapter 7 (Extensive Games with Perfect Information: Extensions and Discussion), then you are ready to tackle Chapters 14 and 15 (Repeated Games). Whichever route you take, you can choose the examples and illustrations to fit one of several themes. You can, for instance, study all the economic examples, or all the political or biological ones. Alternatively, you can build a course around all the examples on a more narrow topic; two possibilities are auction theory and oligopoly theory. All the material is intended to be accessible to undergraduate students. A one-semester course for third or fourth year North American economics majors (who have been exposed to a few of the main ideas in the first and second year courses) could cover up to about half the material in the book in moderate detail. Osbourne and Rubinstein (1994), a graduate text, offers a more advanced treatment of the field. With few exceptions, the two books use the same notation and terminology. The exceptions are noted on the website for this book.