COMBINATORIAL GAMES: TIC-TAC-TOE THEORY (ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS)

JÃ ZSEF BECK

ISBN 10: 0521184754 / ISBN 13: 9780521184755

Published by Cambridge University Press, 2011

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Bibliographic Details

• Title: COMBINATORIAL GAMES: TIC-TAC-TOE THEORY (ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS)
• Publisher: Cambridge University Press
• Publication Date: 2011
• Language: English
• ISBN 10: 0521184754
• ISBN 13: 9780521184755
• Binding: Soft cover
• Condition: Brand New

About this title

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 the Author

József 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.