The Mathematics of Games of Strategy

Author: Melvin Dresher
Publisher: Courier Corporation
ISBN: 0486150062
Format: PDF, ePub
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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, ePub
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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.

Mathematics of Games and Gambling

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

The Language of Game Theory

Author: Adam Brandenburger
Publisher: World Scientific
ISBN: 981451344X
Format: PDF, ePub, Docs
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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."

The Compleat Strategyst

Author: J. D. Williams
Publisher: Courier Corporation
ISBN: 0486136841
Format: PDF, Mobi
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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.

Gl ck Logik und Bluff

Author: Jörg Bewersdorff
Publisher: Springer-Verlag
ISBN: 3658217650
Format: PDF, Mobi
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Der Autor hat es in bewundernswerter Weise geschafft, anhand einer Vielzahl bekannter Spiele von Schach über Poker bis Mastermind einen kleinen Einblick in mathematisch so anspruchsvolle Gebiete wie Wahrscheinlichkeitsrechnung, Optimierungstheorie, Kombinatorik und Spieltheorie zu geben. Hierbei werden so gut wie keine mathematischen Vorkenntnisse erwartet, so dass man das Buch auch interessierten Nichtmathematikern wärmstens empfehlen kann. Anspruchsvolle und unerschrockene Leserinnen und Leser werden in den sehr lesenswerten Anmerkungen am Schluss des Buches Hinweise auf weiterführende Literatur finden, anhand derer sie auch tiefer in mathematische Aspekte eindringen können. Ein schönes Buch, ohne wirkliche Konkurrenz auf dem deutschen Markt, und dies zu einem vernünftigen Preis. Zentralblatt MATH Database 1931 - 2002

The Mathematics of Games

Author: John D. Beasley
Publisher: Courier Corporation
ISBN: 048615162X
Format: PDF, Docs
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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.

Two Person Game Theory

Author: Anatol Rapoport
Publisher: Courier Corporation
ISBN: 0486281094
Format: PDF
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Clear, accessible treatment of mathematical models for resolving conflicts in politics, economics, war, business, and social relationships. Topics include strategy, game tree and game matrix, and much more. Minimal math background required. 1970 edition.

A Gentle Introduction to Game Theory

Author: Saul Stahl
Publisher: American Mathematical Soc.
ISBN: 0821813390
Format: PDF, Docs
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The mathematical theory of games was first developed as a model for situations of conflict, whether actual or recreational. It gained widespread recognition when it was applied to the theoretical study of economics by von Neumann and Morgenstern in Theory of Games and Economic Behavior in the 1940s. The later bestowal in 1994 of the Nobel Prize in economics on Nash underscores the important role this theory has played in the intellectual life of the twentieth century. This volume is based on courses given by the author at the University of Kansas. The exposition is ``gentle'' because it requires only some knowledge of coordinate geometry; linear programming is not used. It is ``mathematical'' because it is more concerned with the mathematical solution of games than with their applications. Existing textbooks on the topic tend to focus either on the applications or on the mathematics at a level that makes the works inaccessible to most non-mathematicians. This book nicely fits in between these two alternatives. It discusses examples and completely solves them with tools that require no more than high school algebra. In this text, proofs are provided for both von Neumann's Minimax Theorem and the existence of the Nash Equilibrium in the $2 \times 2$ case. Readers will gain both a sense of the range of applications and a better understanding of the theoretical framework of these two deep mathematical concepts.

Chases and Escapes

Author: Paul J. Nahin
Publisher: Princeton University Press
ISBN: 0691155011
Format: PDF, ePub, Mobi
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Ideal both for self-study and as supplemental readings by students and/or professors in any of the mathematical and physical sciences, this text presents the historical development of the differential equations of pursuit theory.