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Informationen zum Autor 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. Klappentext A comprehensive and unique volume by the master of combinatorial game theory. Zusammenfassung 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. Inhaltsverzeichnis Preface; A summary of the book in a nutshell; Part I. Weak Win and Strong Draw: 1. Win vs. weak win; 2. The main result: exact solutions for infinite classes of games; Part II. Basic Potential Technique - Game-Theoretic First and Second Moments: 3. Simple applications; 4. Games and randomness; Part III. Advanced Weak Win - Game-Theoretic Higher Moment: 5. Self-improving potentials; 6. What is the Biased Meta-Conjecture, and why is it so difficult?; Part IV. Advanced Strong Draw - Game-Theoretic Independence: 7. BigGame-SmallGame decomposition; 8. Advanced decomposition; 9. Game-theoretic lattice-numbers; 10. Conclusion; 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; Appendix E. New results; Complete list of the open problems; What kinds of games? A dictionary; Dictionary of the phrases and concepts; References.
