| Preface |
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| A summary of the book in a nutshell 1 |
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| PART A WEAK WIN AND STRONG DRAW 15 |
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Chapter I Win vs. Weak Win 17 |
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1 Illustration: every finite point set in the plane is a Weak Winner 19 |
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2 Analyzing the proof of Theorem 1.1 32 |
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3 Examples: Tic-Tac-Toe games 42 |
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4 More examples: Tic-Tac-Toe like games 59 |
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5 Games on hypergraphs, and the combinatorial chaos 72 |
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Chapter II The main result: exact solutions for infinite classes of games 91 |
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6 Ramsey Theory and Clique Games 92 |
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7 Arithmetic progressions 106 |
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8 Two-dimensional arithmetic progressions 118 |
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9 Explaining the exact solutions: a Meta-Conjecture 131 |
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10 Potentials and the Erdos–Selfridge Theorem 146 |
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12 Ramsey Theory and Hypercube Tic-Tac-Toe 172 |
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| PART B BASIC POTENTIAL TECHNIQUE – GAME- THEORETIC FIRST AND SECOND MOMENTS 193 |
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Chapter III Simple applications 195 |
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13 Easy building via Theorem 1.2 196 |
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14 Games beyond Ramsey Theory 204 |
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15 A generalization of Kaplansky's game 216 |
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Chapter IV Games and randomness 230 |
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16 Discrepancy Games and the variance 231 |
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17 Biased Discrepancy Games: when the extension from fair to biased works! 245 |
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18 A simple illustration of "randomness" (I) 260 |
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19 A simple illustration of "randomness" (II) 270 |
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20 Another illustration of "randomness" in games 286 |
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| PART C ADVANCED WEAK WIN – GAME-THEORETIC HIGHER MOMENT 305 |
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Chapter V Self-improving potentials 307 |
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21 Motivating the probabilistic approach 308 |
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22 Game-theoretic second moment: application to the Picker–Chooser game 320 |
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23 Weak Win in the Lattice Games 329 |
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24 Game-theoretic higher moments 340 |
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25 Exact solution of the Clique Game (I) 352 |
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27 Who-scores-more games 372 |
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Chapter VI What is the Biased Meta-Conjecture, and why is it so difficult? 380 |
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28 Discrepancy games (I) 381 |
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29 Discrepancy games (II) 392 |
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30 Biased Games (I): Biased Meta-Conjecture 400 |
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31 Biased games (II): Sacrificing the probabilistic intuition to force negativity 418 |
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32 Biased games (II1): Sporadic results 430 |
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33 Biased games (IV): More sporadic results 439 |
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| PART D ADVANCED STRONG DRAW – GAME-THEORETIC INDEPENDENCE 459 |
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Chapter VII BigGame–SmallGame Decomposition 461 |
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34 The Hales–Jewett Conjecture 462 |
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35 Reinforcing the Erd6s–Selfridge technique (I) 470 |
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36 Reinforcing the Erd6s–Selfridge technique (II) 479 |
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37 Almost Disjoint hypergraphs 485 |
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38 Exact solution of the Clique Game (II) 492 |
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Chapter VIII Advanced decomposition 504 |
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39 Proof of the second Ugly Theorem 505 |
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40 Breaking the "square-root barrier" (I) 525 |
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41 Breaking the "square-root barrier" (II) 536 |
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42 Van der Waerden Game and the RELARIN technique 545 |
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Chapter IX Game-theoretic lattice-numbers 552 |
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43 Winning planes: exact solution 553 |
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44 Winning lattices: exact solution 575 |
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45 I-Can-You-Can't Games – Second Player's Moral Victory 592 |
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46 More exact solutions and more partial results 611 |
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49 Concluding remarks 644 |
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| Appendix A Ramsey Numbers 658 |
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| Appendix B Hales–Jewett Theorem: Shelah's proof 669 |
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| Appendix C A formal treatment of Positional Games 677 |
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| Appendix D An informal introduction to game theory 705 |
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| Complete list of the Open Problems 716 |
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| What kinds of games? A dictionary 724 |
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| Dictionary of the phrases and concepts 727 |
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| References 730 |
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Lisainfo e-raamatute kohta