# Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction

## Synopsis

Since its original publication in 2000, Game Theory Evolving has been considered the best textbook on evolutionary game theory. This completely revised and updated second edition of Game Theory Evolving contains new material and shows students how to apply game theory to model human behavior in ways that reflect the special nature of sociality and individuality. The textbook continues its in-depth look at cooperation in teams, agent-based simulations, experimental economics, the evolution and diffusion of preferences, and the connection between biology and economics.

Recognizing that students learn by doing, the textbook introduces principles through practice. Herbert Gintis exposes students to the techniques and applications of game theory through a wealth of sophisticated and surprisingly fun-to-solve problems involving human and animal behavior. The second edition includes solutions to the problems presented and information related to agent-based modeling. In addition, the textbook incorporates instruction in using mathematical software to solve complex problems. Game Theory Evolving is perfect for graduate and upper-level undergraduate economics students, and is a terrific introduction for ambitious do-it-yourselfers throughout the behavioral sciences.

• Revised and updated edition relevant for courses across disciplines

• Solutions to problems presented throughout

• Incorporates instruction in using computational software for complex problem solving

• Includes in-depth discussions of agent-based modeling

## Excerpt

Was sich sagen läßt, läßt sich klar sagen, und wovon man nicht
sprechen kann, darüber muß man schweigen.

Ludwig Wittgenstein

This book is a problem-centered introduction to classical and evolutionary game theory. For most topics, I provide just enough in the way of definitions, concepts, theorems, and examples to begin solving problems. Learning and insight come from grappling with and solving problems. I provide extensive answers to some problems, sketchy and suggestive answers to most others. Students should consult the answers in the back of the book only to check their work. If a problem seems too difficult to solve, the student should come back to it a day, a week, or a month later, rather than peeking at the solution.

Game theory is logically demanding, but on a practical level, it requires surprisingly few mathematical techniques. Algebra, calculus, and basic probability theory suffice. However, game theory frequently requires considerable notation to express ideas clearly. The reader should commit to memory the precise definition of every term, and the precise statement of most theorems.

Clarity and precision do not imply rigor. I take my inspiration from physics, where sophisticated mathematics is common, but mathematical rigor is considered an impediment to creative theorizing. I stand by the truth and mathematical cogency of the arguments presented in this book, but not by their rigor. Indeed, the stress placed on game-theoretic rigor in recent years is misplaced. Theorists could worry more about the empirical relevance of their models and take less solace in mathematical elegance.

For instance, if a proposition is proved for a model with a finite number of agents, it is completely irrelevant whether it is true for an infinite number of agents. There are, after all, only a finite number of people, or even bacteria. Similarly, if something is true in games in which payoffs are finitely divisible (e.g., there is a minimum monetary unit), it does not matter whether it is true when payoffs are infinitely divisible. There are no payoffs in the universe, as far as we know, that are infinitely divisible. Even time . . .

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