Game theory basics

著者

    • Von Stengel, Bernhard

書誌事項

Game theory basics

Bernhard von Stengel

Cambridge University Press, [2021]

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注記

Content Type: text (rdacontent), Media Type: unmediated (rdamedia), Carrier Type: volume (rdacarrier)

Includes bibliographical references and index

Summary: "This book is an introduction to the mathematics of non-cooperative game theory. Each concept is explained in detail, starting from a main example, with a slowpaced proof of each theorem. The book has been designed and tested for self-study, and as an undergraduate course text with core chapters and optional chapters for different audiences. It has been developed over 15 years for a one-semester course on game theory at the London School of Economics and the distance learning program of the University of London, attended each year by about 200 third-year students in mathematics, economics, management, and other degrees. After studying this book, a student who started from first-year mathematics (the basics of linear algebra, analysis, and probability) will have a solid understanding of the most important concepts and theorems of non-cooperative game theory"-- Provided by publisher

内容説明・目次

内容説明

Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.

目次

  • 1. Nim and Combinatorial Games
  • 2. Congestion Games
  • 3. Games in Strategic Form
  • 4. Game Trees with Perfect Information
  • 5. Expected Utility
  • 6. Mixed Equilibrium
  • 7. Brouwer's Fixed-Point Theorem
  • 8. Zero-Sum Games
  • 9. Geometry of Equilibria in Bimatrix Games
  • 10. Game Trees with Imperfect Information
  • 11. Bargaining
  • 12. Correlated Equilibrium.

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