Combinatorial Games: Tic-Tac-Toe Theory: 114 (Encyclopedia of Mathematics and its Applications, Series Number 114) - Softcover

Beck, József

Softcover

ISBN 10: 0521184754 ISBN 13: 9780521184755

Publisher: Cambridge University Press, 2011

Synopsis

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, József 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.

About this title

Review

'... 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 Newsletter

Book Description

In this comprehensive volume, József Beck shows readers how to escape from the combinatorial chaos arising in the analysis of many games by using the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Striking results are obtained and new duality principles discovered.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2011
• ISBN 10: 0521184754
• ISBN 13: 9780521184755
• Binding: Paperback
• Language: English
• Number of pages: 748