Combinatorial Games

Tic-Tac-Toe Theory

By: JÃ³zsef Beck

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Paperback | 28 April 2011

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748 Pages

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23.39 x 15.6 x 3.79

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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.

Industry Reviews

'... 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

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Preface
A summary of the book in a nutshell
Weak Win and Strong Draw:
Win vs. weak win
The main result: exact solutions for infinite classes of games
Basic Potential Technique - Game-Theoretic First and Second Moments:
Simple applications
Games and randomness
Advanced Weak Win - Game-Theoretic Higher Moment:
Self-improving potentials
What is the Biased Meta-Conjecture, and why is it so difficult?
Advanced Strong Draw - Game-Theoretic Independence:
BigGame-SmallGame decomposition
Advanced decomposition
Game-theoretic lattice-numbers
Conclusion
Ramsey numbers
Hales-Jewett theorem: Shelah's proof
A formal treatment of positional games
An informal introduction to game theory
New results
Complete list of the open problems
What kinds of games? A dictionary
Dictionary of the phrases and concepts
References
Table of Contents provided by Publisher. All Rights Reserved.

Combinatorial Games

Tic-Tac-Toe Theory

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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