Combinatorial Game Theory
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Lessons In Play
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Author : Michael Albert
language : en
Publisher: CRC Press
Release Date : 2007-07-02
Lessons In Play written by Michael Albert and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-02 with Mathematics categories.
Combinatorial games are games of pure strategy involving two players, with perfect information and no element of chance. Starting from the very basics of gameplay and strategy, the authors cover a wide range of topics, from game algebra to special classes of games. Classic techniques are introduced and applied in novel ways to analyze both old and
Combinatorial Game Theory
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Author : Aaron N. Siegel
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-20
Combinatorial Game Theory written by Aaron N. Siegel and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.
It is wonderful to see advanced combinatorial game theory made accessible. Siegel's expertise and enjoyable writing style make this book a perfect resource for anyone wanting to learn the latest developments and open problems in the field. —Erik Demaine, MIT Aaron Siegel has been the major contributor to Combinatorial Game Theory over the last decade or so. Now, in this authoritative work, he has made the latest results in the theory accessible, so that the subject will achieve the place in mathematics that it deserves. —Richard Guy, University of Calgary Combinatorial game theory is the study of two-player games with no hidden information and no chance elements. The theory assigns algebraic values to positions in such games and seeks to quantify the algebraic and combinatorial structure of their interactions. Its modern form was introduced thirty years ago, with the publication of the classic Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy, and interest has rapidly increased in recent decades. This book is a comprehensive and up-to-date introduction to the subject, tracing its development from first principles and examples through many of its most recent advances. Roughly half the book is devoted to a rigorous treatment of the classical theory; the remaining material is an in-depth presentation of topics that appear for the first time in textbook form, including the theory of misère quotients and Berlekamp's generalized temperature theory. Packed with hundreds of examples and exercises and meticulously cross-referenced, Combinatorial Game Theory will appeal equally to students, instructors, and research professionals. More than forty open problems and conjectures are mentioned in the text, highlighting the many mysteries that still remain in this young and exciting field. Aaron Siegel holds a Ph.D. in mathematics from the University of California, Berkeley and has held positions at the Mathematical Sciences Research Institute and the Institute for Advanced Study. He was a partner at Berkeley Quantitative, a technology-driven hedge fund, and is presently employed by Twitter, Inc.
Lessons In Play
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Author : Michael H. Albert
language : en
Publisher: CRC Press
Release Date : 2019-04-30
Lessons In Play written by Michael H. Albert and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-30 with Mathematics categories.
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
Cooperative Game Theory And Applications
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Author : Imma Curiel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Cooperative Game Theory And Applications written by Imma Curiel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Business & Economics categories.
In this book applications of cooperative game theory that arise from combinatorial optimization problems are described. It is well known that the mathematical modeling of various real-world decision-making situations gives rise to combinatorial optimization problems. For situations where more than one decision-maker is involved classical combinatorial optimization theory does not suffice and it is here that cooperative game theory can make an important contribution. If a group of decision-makers decide to undertake a project together in order to increase the total revenue or decrease the total costs, they face two problems. The first one is how to execute the project in an optimal way so as to increase revenue. The second one is how to divide the revenue attained among the participants. It is with this second problem that cooperative game theory can help. The solution concepts from cooperative game theory can be applied to arrive at revenue allocation schemes. In this book the type of problems described above are examined. Although the choice of topics is application-driven, it also discusses theoretical questions that arise from the situations that are studied. For all the games described attention will be paid to the appropriateness of several game-theoretic solution concepts in the particular contexts that are considered. The computation complexity of the game-theoretic solution concepts in the situation at hand will also be considered.
An Introduction To Combinatorial Game Theory
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Author : L. R. Haff
language : en
Publisher:
Release Date : 2016-06-02
An Introduction To Combinatorial Game Theory written by L. R. Haff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Education categories.
An introductory text to the area of mathematics known as Combinatorial Game Theory. Starting with Nim, a variety of combinatorial games are introduced as well as the tools to analyze them.
Matt Devos And Deborah A Kent
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Author : Matt DeVos
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-27
Matt Devos And Deborah A Kent written by Matt DeVos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-27 with Mathematics categories.
This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning. Designed as a textbook for an undergraduate mathematics class and with ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the generous sets of exercises at various levels.
Mathematical Go
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Author : Elwyn Berlekamp
language : en
Publisher: CRC Press
Release Date : 1994-02-15
Mathematical Go written by Elwyn Berlekamp and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-15 with Mathematics categories.
The ancient game of Go is one of the less obvious candidates for mathematical analysis. With the development of new concepts in combinatorial game theory, the authors have been able to analyze Go games and find solutions to real endgame problems that have stumped professional Go players. Go players with an interest in mathematics and mathematicians
Twenty Lectures On Algorithmic Game Theory
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Author : Tim Roughgarden
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-01
Twenty Lectures On Algorithmic Game Theory written by Tim Roughgarden and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-01 with Computers categories.
Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.
Combinatorial Game Theory
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Author : Aaron N. Siegel
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-01
Combinatorial Game Theory written by Aaron N. Siegel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-01 with Mathematics categories.
Combinatorial game theory is the study of two-player games with no hidden information and no chance elements. The theory assigns algebraic values to positions in such games and seeks to quantify the algebraic and combinatorial structure of their interactions. Its modern form was introduced thirty years ago, with the publication of the classic Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy, and interest has rapidly increased in recent decades. This book is a comprehensive and up-to-date introduction to the subject, tracing its development from first principles and examples through many of its most recent advances. Roughly half the book is devoted to a rigorous treatment of the classical theory; the remaining material is an in-depth presentation of topics that appear for the first time in textbook form, including the theory of misère quotients and Berlekamp's generalized temperature theory. Packed with hundreds of examples and exercises and meticulously cross-referenced, Combinatorial Game Theory will appeal equally to students, instructors, and research professionals. More than forty open problems and conjectures are mentioned in the text, highlighting the many mysteries that still remain in this young and exciting field. Aaron Siegel holds a Ph.D. in mathematics from the University of California, Berkeley and has held positions at the Mathematical Sciences Research Institute and the Institute for Advanced Study. He was a partner at Berkeley Quantitative, a technology-driven hedge fund, and is presently employed by Twitter, Inc.
Game Theory A Comprehensive Introduction
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Author : Hans Keiding
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-30
Game Theory A Comprehensive Introduction written by Hans Keiding and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-30 with Mathematics categories.
This book is intended as an introduction to game theory which goes beyond the field of application, economics, and which introduces the reader to as many different sides of game theory as possible within the limitations of an introduction. The main goal is to give an impression of the diversity of game theoretical models, while at the same time covering the standard topics. The book has an equal coverage of non-cooperative and cooperative games, and it covers several topics such as selecting Nash equilibria, non-transferable utility games, applications of game theory to logic, combinatorial and differential games.