Preface
Game theory is the mathematical study of interaction among independent, self-interested agents. It is studied primarily by mathematicians and economists, microeconomics being its main initial application area. So what business do two computer scientists have publishing a text on game theory?
The origin of this booklet is our much longer book, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, which covers diverse theories relevant to the broad area of Multiagent Systems within Artificial Intelligence (AI) and other areas of computer science. Like many other disciplines, computer science—and in particular AI—have been profoundly influenced by game theory, with much back and forth between the fields taking place in recent years. And so it is not surprising to find that Multiagent Systems contains a fair bit of material on game theory. That material can be crudely divided into two kinds: basics, and more advanced material relevant to AI and computer science. This booklet weaves together the material of the first kind.
Many textbooks on game theory exist, some of them superb. The serious student of game theory cannot afford to neglect those, and in the final chapter we provide some references. But the audience for game theory has grown dramatically in recent years, spanning disciplines as diverse as political science, biology, psychology, linguistics, sociology—and indeed computer science—among many others. What has been missing is a relatively short introduction to the field covering the common basis that any one interested in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This booklet aims to fill this gap. It is the book we wish we had had when we first ventured into the field.
We should clarify what we mean by “essentials.” We cover the main classes of games, their representations, and the main concepts used to analyze them (so-called “solution concepts"). We cannot imagine any consumer of game theory who will not require a solid grounding in each of these topics. We discuss them in sufficient depth to provide this grounding, though of course much more can be said about each of them. This leaves out many topics in game theory that are key in certain applications, but not in all. Some examples are computational aspects of games and computationally motivated representations, learning in games, and mechanism design (in particular, auction theory). By omitting these topics we do not mean to suggest that they are unimportant, only that they will not be equally relevant to everyone who finds use for game theory. The reader of this booklet will likely be grounded in a particular discipline, and will thus need to augment his or her reading with material essential to that discipline.
This book makes an appropriate text for an advanced undergraduate course or a game theory unit in a graduate course. The book’s Web site
contains additional resources for both students and instructors.
A final word on pronouns and gender. We use male pronouns to refer to agents throughout the book. We debated this between us, not being happy with any of the alternatives. In the end we reluctantly settled on the “standard” male convention rather than the reverse female convention or the grammatically-dubious “they.” We urge the reader not to read patriarchal intentions into our choice.