Game Theory & Study, Computer Science & Combinatorics, Mathematical Programming & Operations Research

Combinatorial Games: Tic-Tac-Toe Theory

Name: Combinatorial Games: Tic-Tac-Toe Theory
Author: Jozsef Beck
ISBN: 9780521184755

by Jozsef Beck

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Overview

"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. This is the subject of combinatorial game theory. Most board games are a challenge for mathematics: to analyze a position one has to examine the available options, and then the further options available after selecting any option, and so on. This leads to 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.

About the Author, Jozsef Beck

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.

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Editorials

From the Publisher

"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

"József 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