Lessons in Play : An Introduction to Combinatorial Game Theory, Second Edition book cover
2nd Edition

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





ISBN 9781482243031
Published April 22, 2019 by A K Peters/CRC Press
346 Pages 148 B/W Illustrations

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Book Description

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


Table of Contents

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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Author(s)

Biography

Michael Albert - University of Otago



Richard Nowakowski - Dalhousie University



David Wolfe - Dalhousie University