دانلود کتاب Combinatorial games

فهرست مطالب :

Content: 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.
Abstract: