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## Details

Material Type: | Internet resource |
---|---|

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
József Beck |

ISBN: | 9780521461009 0521461006 |

OCLC Number: | 175284055 |

Description: | xiv, 732 pages : illustrations ; 24 cm. |

Contents: | pt. A. Weak win and strong draw -- ch. I. Win vs. weak win -- Illustration : every finite point set in the plane is a weak winner -- Analyzing the proof of theorem 1.1 -- Examples : tic-tac-toe games -- More examples : tic-tac-toe like games -- Games on hypergraphs, and the combinatorial chaos -- ch. II. The main result : exact solutions for infinite classes of games -- Ramsey theory and clique games -- Arithmetic progressions -- Two-dimensional arithmetic progressions -- Explaining the exact solutions : a meta-conjecture -- Potentials and the Erdős-Selfridge theorem -- Local vs. global -- Ramsey theory and hypercube tic-tac-toe -- pt. B. Basic potential technique : game-theoretic first and second moments -- ch. III. Simple applications -- Easy building via theorem 1.2 -- Games beyond Ramsey theory -- A generalization of Kaplansky's game -- ch. IV. Games and randomness -- Discrepancy games and the variance -- Biased discrepancy games : when the extension from fair to biased works! -- A simple illustration of "randomness" (I) -- A simple illustration of "randomness" (II) -- Another illustration of "randomness" in games. pt. C. Advanced weak win : game-theoretic higher moment -- ch. V. Self-improving potentials -- Motivating the probabilistic approach -- Game-theoretic second moment : application to the picker-choose game -- Weak win in the lattice games -- Game-theoretic higher moments -- Exact solution of the clique game (I) -- More applications -- Who-scores-more games -- ch. VI. What is the biased meta-conjecture, and why is it so difficult? -- Discrepancy games (I) -- Discrepancy games (II) -- Biased games (I) : biased meta-conjecture -- Biased games (II) : sacrificing the probabilistic intuition to force negativity -- Biased games (III) : sporadic results -- Biased games (IV) : more sporadic results -- pt. D. Advanced strong draw : game-theoretic independence -- ch. VII. BigGame-SmallGame decomposition -- The Hales-Jewett conjecture -- Reinforcing the Erdős-Selfridge technique (I) -- Reinforcing the Erdős-Selfridge technique (II) -- Almost disjoint hypergraphs -- Exact solution of the clique game (II). ch. VIII. Advanced decomposition -- Proof of the second ugly theorem -- Breaking the "square-root barrier" (I) -- Breaking the "square-root barrier" (II) -- Van der Waerden game and the RELARIN technique -- ch. IX. Game-theoretic lattice-numbers -- Winning planes : exact solution -- Winning lattices : exact solution -- I-can-you-can't games -- second player's moral victory -- ch. X. Conclusion -- More exact solutions and more partial results -- Miscellany (I) -- Miscellany (II) -- Concluding remarks -- 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. |

Series Title: | Encyclopedia of mathematics and its applications, v. 114. |

Responsibility: | József Beck. |

More information: |

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## Reviews

*Editorial reviews*

Publisher Synopsis

'... 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 "This is an excellent, extensive, and readable review of combinatorial game theory... The book, which is very hard to put down, ends with an extremely helpful dictionary and list of open problems." M. Bona, University of Florida for CHOICE "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 "Jozsef Beck has done a tremendous amount of work in this area. Many results appear in this book for the first time. This is a great book that brings many (all?) of the results in this field under one roof." William Gasarch for SIGACT News Read more...

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by ddolby updated 2016-01-12