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.
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.
