2nd Edition

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

    346 Pages 148 B/W Illustrations
    by A K Peters/CRC Press

    346 Pages 148 B/W Illustrations
    by A K Peters/CRC Press

    344 Pages 148 B/W Illustrations
    by A K Peters/CRC Press

    This second edition of Lessons in Play reorganizes the presentation of the popular original text in combinatorial game theory to make it even more widely accessible. Starting with a focus on the essential concepts and applications, it then moves on to more technical material. Still written in a textbook style with supporting evidence and proofs, the authors add many more exercises and examples and implement a two-step approach for some aspects of the material involving an initial introduction, examples, and basic results to be followed later by more detail and abstract results.



    Features







    • Employs a widely accessible style to the explanation of combinatorial game theory






    • Contains multiple case studies






    • Expands further directions and applications of the field






    • Includes a complete rewrite of CGSuite material


    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

    Biography

    Michael Albert - University of Otago



    Richard Nowakowski - Dalhousie University



    David Wolfe - Dalhousie University