Combinatorial Games
Tic-Tac-Toe Theory
Published on 20. March 2008
Book
Hardback
748 pages
978-0-521-46100-9 (ISBN)
Description
Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, solitaire and hex. The main challenge of combinatorial game theory is to handle combinatorial chaos, where brute force study is impractical. In this comprehensive volume, Jozsef Beck shows readers how to escape from the combinatorial chaos via the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Using this, the author is able to determine the exact results about infinite classes of many games, leading to the discovery of some striking new duality principles. Available for the first time in paperback, it includes a new appendix to address the results that have appeared since the book's original publication.
Reviews / Votes
'... this book is a milestone in Game Theory, it will become a classic ...' Acta Scientiarum Mathematicarum '... a most thorough and useful treatment of the subject (so far insufficiently presented in the literature) with an enormous store of results, links with other theories, and interesting open problems.' A. Pultr, Mathematical Reviews 'This seems to be the best and most useful treatment of the subject so far ... The book is recommended for a broad mathematical audience. Almost all concepts from other parts of mathematics are explained so it is convenient both for the specialist seeking a detailed survey of the topic and for students hoping to learn something new about the subject. The book has a potential to become a milestone in the development of combinatorial game theory.' EMS NewsletterMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 170 Line drawings, unspecified
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 44 mm
Weight
1274 gr
ISBN-13
978-0-521-46100-9 (9780521461009)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
04/2011
Cambridge University Press
€107.90
Shipment within 15-20 days
E-Book
02/2011
1st Edition
Cambridge University Press
€82.99
Available for download
Person
Jozsef Beck is a Professor in the Mathematics Department of Rutgers University. He has received the Fulkerson Prize for Research in Discrete Mathematics and has written around 100 research publications. He is the co-author, with W. L. Chen, of the pioneering monograph Irregularities of Distribution.
Content
Preface; A summary of the book in a nutshell; Part I. Weak Win and Strong Draw: 1. Win vs. weak win; 2. The main result: exact solutions for infinite classes of games; Part II. Basic Potential Technique - Game-Theoretic First and Second Moments: 3. Simple applications; 4. Games and randomness; Part III. Advanced Weak Win - Game-Theoretic Higher Moment: 5. Self-improving potentials; 6. What is the Biased Meta-Conjecture, and why is it so difficult?; Part IV. Advanced Strong Draw - Game-Theoretic Independence: 7. BigGame-SmallGame decomposition; 8. Advanced decomposition; 9. Game-theoretic lattice-numbers; 10. Conclusion; Appendix A. Ramsey numbers; Appendix B. Hales-Jewett theorem: Shelah's proof; Appendix C. A formal treatment of positional games; Appendix D. An informal introduction to game theory; Appendix E. New results; Complete list of the open problems; What kinds of games? A dictionary; Dictionary of the phrases and concepts; References.