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Combinatorial games : tic-tac-toe theory /
"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 com...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2008.
|
| Colección: | Encyclopedia of mathematics and its applications ;
v. 114. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.