The Mathematics of Games of Strategy

Author: Melvin Dresher
Publisher: Courier Corporation
ISBN: 0486150062
Format: PDF, Mobi
Download Now
This text offers an exceptionally clear presentation of the mathematical theory of games of strategy and its applications to many fields including economics, military, business, and operations research.

Chance Strategy and Choice

Author: Samuel Bruce Smith
Publisher: Cambridge University Press
ISBN: 1316033708
Format: PDF
Download Now
Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague–Grundy theorem and Arrow's impossibility theorem. • Uses an integrative approach to probability, game, and social choice theory • Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies • Contains numerous exercises and examples of varying levels of difficulty • Requires only a high school mathematical background.

The Mathematics of Games and Gambling

Author: Edward W. Packel
Publisher: MAA
ISBN: 9780883856284
Format: PDF, Kindle
Download Now
This book shows you what determines the best bet in a game of chance or the optimal strategy in a strategic game.

The Mathematics of Games

Author: John D. Beasley
Publisher: Courier Corporation
ISBN: 048615162X
Format: PDF, ePub, Mobi
Download Now
Lucid, instructive, and full of surprises, this book examines how simple mathematical analysis can throw unexpected light on games of every type, from poker to golf to the Rubik's cube. 1989 edition.

Gl ck Logik und Bluff

Author: Jörg Bewersdorff
Publisher: Springer-Verlag
ISBN: 3663108139
Format: PDF, ePub
Download Now
Glück, Logik und Bluff - drei Begriffe, die abhängig vom Charakter eines Gesellschaftsspieles Wege zum Gewinn weisen. Eng damit verbunden sind drei mathematische Theorien: Die Wahrscheinlichkeitsrechung erlaubt es, die Gewinnchancen in Glücksspielen zu kalkulieren. Von Algorithmen, wie sie auch Schachcomputern zugrundeliegen, handelt die Theorie der kombinatorischen Spiele. Ganz andere Optimierungsansätze, nämlich solche aus der mathematischen Spieltheorie, sind gefragt, wenn Mitspieler wie bei Kartenspielen unterschiedliche Informationsstände über den erreichten Spielstand haben. Anhand vielfältiger (Bei-) Spiele werden Teile der drei Theorien vorgestellt.

The Language of Game Theory

Author: Adam Brandenburger
Publisher: World Scientific
ISBN: 9814513458
Format: PDF, ePub
Download Now
This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make how players reason about a game a central feature of the theory. The program — now called epistemic game theory — extends the classical definition of a game model to include not only the game matrix or game tree, but also a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determine the implications of how players reason for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior. Contents:An Impossibility Theorem on Beliefs in Games (Adam Brandenburger and H Jerome Keisler)Hierarchies of Beliefs and Common Knowledge (Adam Brandenburger and Eddie Dekel)Rationalizability and Correlated Equilibria (Adam Brandenburger and Eddie Dekel)Intrinsic Correlation in Games (Adam Brandenburger and Amanda Friedenberg)Epistemic Conditions for Nash Equilibrium (Robert Aumann and Adam Brandenburger)Lexicographic Probabilities and Choice Under Uncertainty (Lawrence Blume, Adam Brandenburger, and Eddie Dekel)Admissibility in Games (Adam Brandenburger, Amanda Friedenberg and H Jerome Keisler)Self-Admissible Sets (Adam Brandenburger and Amanda Friedenberg) Readership: Graduate students and researchers in the fields of game theory, theoretical computer science, mathematical logic and social neuroscience. Keywords:Game Theory;Epistemic Game Theory;Foundations;Applied Mathematics;Social Neuroscience;Rationalizability;Nash Equilibrium;Probability;UncertaintyKey Features:Focuses on epistemic game theory — an emerging approach to game theoryLikely strong interest in these tools from other disciplines, includingtheoretical computer science, mathematical logic, and social neuroscienceProminent co-author team: Robert Aumann (Hebrew University, Nobel Laureate 2005); Lawrence Blume (Cornell University); Eddie Dekel (Northwestern University and Tel Aviv University); Amanda Freedeneurg (Arizona State University); H Jerome Keisler (University of Wisconsin Madison)Reviews: "Adam Brandenburger's work on the knowledge requirements implicit in game theory has become classic. These are of profound importance in understanding the relevance of game theory and, indeed, economic theory in general to the real economy. It is very good to have them collected, with an introduction that brings out the underlying themes." Kenneth J Arrow Stanford University, USA "Over the past decade epistemic game theory has emerged as one of the principled alternatives to more traditional approaches to economic interactions and Adam Brandenburger has played a central role in that emergence. For anyone interested in epistemic game theory, or game theory in general, this book is a must have. But even more important is the opportunity this volume, and epistemic game theory in general, presents to empirical scientists. As Brandenburger notes in his Introduction, until now epistemic game theory has been a theoretical discipline. This volume should make it clear, however, that it could be — and likely soon will be — an empirical undertaking. Anyone interested in behavioral, psychological, or neurobiological studies of how we make decisions during strategic play will find in this volume a profoundly fascinating set of empirically testable hypotheses just waiting to be examined." Paul Glimcher New York University, USA "Three hundred years ago, Francis Waldegrave found the first minimax solution of a matrix game. But in his correspondence with mathematicians Pierre Rémond de Montmort and Nicolaus Bernoulli, Waldegrave counseled that epistemic considerations involving knowledge, beliefs, uncertainty, and incomplete information also mattered. The principal practitioners of game theory, with the notable exceptions of John Harsanyi and Robert Aumann, have ignored this advice. In recent years, these two theorists have been joined by Adam Brandenburger, whose work on epistemic game theory has been collected in this splendid volume. Eight classic papers by Brandenburger with a number of co-authors present an authoritative view of the field while an insightful introduction provides a roadmap to research both present and future." Harold W Kuhn Princeton University, USA "This book features a collection of foundational papers by Adam Brandenburger in epistemic game theory. Though still evolving, this approach marks a tectonic shift in game theory by offering a new, epistemic dimension which might be compared to the introduction of synchronized sound to motion pictures in the early 20th century: it might not immediately provide a complete picture, but it has the potential of changing the field forever." Sergei N Artemov The Graduate Center of the City University of New York, USA "Adam Brandenburger has played a leading role in developing the program of epistemic game theory, the goal of which is to provide a deeper and clearer foundation for game theory as a whole. This volume collects a remarkable body of work by Brandenburger and his collaborators, in which penetrating conceptual analysis and the development of a rich mathematical theory go hand in hand. The work offers much of great interest to computer scientists, who will see many connections with their study of recursive and corecursive structures, of processes and their logics, and of multi-agent systems; and to mathematicians and logicians interested in making precise models of the reflexive structures inherent in systems containing rational agents who can reason about the system of which they form a part. I hope that this timely collection will help to stimulate cross-disciplinary work on these fundamental topics." Samson Abramsky Oxford University, UK "Games are playgrounds where players meet and interact, guided by streams of information and opinion. Adam Brandenburger's work has been instrumental in creating a new rich epistemic framework doing justice to both games and their players. This timely book will help a broader audience learn and appreciate the resulting theory." Johan van Benthem University of Amsterdam, The Netherlands and Stanford University, USA "Economics, so grounded in the notion of equilibrium, has required substantial foundational work on reasoning about reasoning — epistemics — in interacting situations (games). Yet, if plain reasoning is difficult enough, just imagine epistemics. Adam Brandenburger, as is evident from the elegant and clear chapters of this book, is a master of the trade. His highly regarded research, always subtle and deep, is of the kind that establishes milestones while at the same time opening up vistas to new, and unexpected, frontiers. This book is specialized, certainly, but it is a must." Andreu Mas-Colell Universitat Pompeu Fabra, Spain “The papers in this book had a huge impact on the field, created an inter– and multi–discipliner research within the intersection of economics, philosophy, mathematics and computer science, and also inspired countless amount of PhD dissertations. Brandenburger's work contains very precise and beautiful mathematics, an earthly reading of epistemics and a puzzling innovation.” Zentralblatt MATH

The Language of Game Theory

Author: Adam Brandenburger
Publisher: World Scientific
ISBN: 981451344X
Format: PDF, ePub, Mobi
Download Now
This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make how players reason about a game a central feature of the theory. The program OCo now called epistemic game theory OCo extends the classical definition of a game model to include not only the game matrix or game tree, but also a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determine the implications of how players reason for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior. Sample Chapter(s). Foreword (39 KB). Introduction (132 KB). Chapter 1: An Impossibility Theorem on Beliefs in Games (299 KB). Contents: An Impossibility Theorem on Beliefs in Games (Adam Brandenburger and H Jerome Keisler); Hierarchies of Beliefs and Common Knowledge (Adam Brandenburger and Eddie Dekel); Rationalizability and Correlated Equilibria (Adam Brandenburger and Eddie Dekel); Intrinsic Correlation in Games (Adam Brandenburger and Amanda Friedenberg); Epistemic Conditions for Nash Equilibrium (Robert Aumann and Adam Brandenburger); Lexicographic Probabilities and Choice Under Uncertainty (Lawrence Blume, Adam Brandenburger, and Eddie Dekel); Admissibility in Games (Adam Brandenburger, Amanda Friedenberg and H Jerome Keisler); Self-Admissible Sets (Adam Brandenburger and Amanda Friedenberg). Readership: Graduate students and researchers in the fields of game theory, theoretical computer science, mathematical logic and social neuroscience."

Probability Guide to Gambling

Author: Catalin Barboianu
Publisher: INFAROM Publishing
ISBN: 9738752035
Format: PDF, ePub, Docs
Download Now
Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability (definitions, properties, theorems and calculus formulas), combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one (like many other titles published on this subject), but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal."

Mathematics of Games and Gambling

Author: Edward W. Packel
Publisher: MAA
ISBN: 9780883856468
Format: PDF, Mobi
Download Now
The new edition of a favourite, featuring fresh material such as betting in sport and bluffing in poker.

The Compleat Strategyst

Author: J. D. Williams
Publisher: Courier Corporation
ISBN: 0486136841
Format: PDF, ePub, Mobi
Download Now
Only a basic understanding of arithmetic is needed to grasp these strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.