Lessons in Play - Michael Albert, Richard Nowakowski, David Wolfe

Lessons in Play

An Introduction to Combinatorial Game Theory, Second Edition
Buch | Softcover
346 Seiten
2023 | 2nd edition
Taylor & Francis Ltd (Verlag)
978-1-032-47566-0 (ISBN)
54,85 inkl. MwSt
A thorough revision of a popular text in combinatorial game theory, this second edition reorganizes presentation to make it more widely accessible.
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

Michael Albert - University of Otago Richard Nowakowski - Dalhousie University David Wolfe - Dalhousie University

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

Erscheinungsdatum
Zusatzinfo 148 Illustrations, black and white
Verlagsort London
Sprache englisch
Maße 156 x 234 mm
Gewicht 612 g
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Finanz- / Wirtschaftsmathematik
ISBN-10 1-032-47566-8 / 1032475668
ISBN-13 978-1-032-47566-0 / 9781032475660
Zustand Neuware
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