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  • Lessons in Play: An Introduction to Combinatorial Game Theory, Second Edition

    • Item No : 146281193022
    • Condition : Brand New
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    • Current Bid : US $60.61
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    • Combinatorial Games



      0.1 Basic Terminology



      Problems



      1 Basic Techniques



      1.1 Greedy



      1.2 Symmetry



      1.3 Parity



      1.4 Give Them Enough Rope!



      1.5 Strategy Stealing



      1.6 Change the Game!



      1.7 Case Study: Long Chains in Dots & Boxes



      Problems



      2 Outcome Classes



      2.1 Outcome Functions



      2.2 Game Positions and Options



      2.3 Impartial Games: Minding Your Ps and Ns



      2.4 Case Study: Roll The Lawn



      2.5 Case Study: Timber



      2.6 Case Study: Partizan Endnim



      Problems



      3 Motivational Interlude: Sums of Games



      3.1 Sums



      3.2 Comparisons



      3.3 Equality and Identity



      3.4 Case Study: Domineering Rectangles



      Problems



      4 The Algebra of Games



      4.1 The Fundamental Definitions



      4.2 Games Form a Group with a Partial Order



      4.3 Canonical Form



      4.4 Case Study: Cricket Pitch



      4.5 Incentives



      Problems



      5 Values of Games



      5.1 Numbers



      5.2 Case Study: Shove



      5.3 Stops



      5.4 A Few All-Smalls: Up, Down, and Stars



      5.5 Switches



      5.6 Case Study: Elephants & Rhinos



      5.7 Tiny and Miny



      5.8 Toppling Dominoes



      5.9 Proofs of Equivalence of Games and Numbers



      Problems



      6 Structure



      6.1 Games Born by Day 2



      6.2 Extremal Games Born By Day n



      6.3 More About Numbers



      6.4 The Distributive Lattice of Games Born by Day n



      6.5 Group Structure



      Problems



      7 Impartial Games



      7.1 A Star-Studded Game



      7.2 The Analysis of Nim



      7.3 Adding Stars



      7.4 A More Succinct Notation



      7.5 Taking-and-Breaking Games



      7.6 Subtraction Games



      7.7 Keypad Games



      Problems



      8 Hot Games



      8.1 Comparing Games and Numbers



      8.2 Coping with Confusion



      8.3 Cooling Things Down



      8.4 Strategies for Playing Hot Games



      8.5 Norton Products



      Problems



      9 All-Small Games



      9.1 Cast of Characters



      9.2 Motivation: The Scale of Ups



      9.3 Equivalence Under



      9.4 Atomic Weight



      9.5 All-Small Shove



      9.6 More Toppling Dominoes



      9.7 Clobber



      Problems



      10 Trimming Game Trees



      10.1 Introduction



      10.2 Reduced Canonical Form



      10.3 Hereditary-Transitive Games



      10.4 Ordinal Sum



      10.5 Stirling-Shave



      10.6 Even More Toppling Dominoes



      Problems



      Further Directions



      1 Transfinite Games



      2 Algorithms and Complexity



      3 Loopy Games



      4 Kos: Repeated Local Positions



      5 Top-Down Thermography



      6 Enriched Environments



      7 Idempotents



      8 Mis`ere Play



      9 Scoring Games



      A Top-Down Induction



      A.1 Top-Down Induction



      A.2 Examples

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