# An Introductory Course On Mathematical Game Theory

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## An Introductory Course on Mathematical Game Theory

Author | : Julio González-Díaz,Ignacio García-Jurado,M. Gloria Fiestras-Janeiro |

Publsiher | : American Mathematical Soc. |

Total Pages | : 324 |

Release | : 2010 |

ISBN | : 0821851519 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**An Introductory Course on Mathematical Game Theory Book Excerpt:**

Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research. The book is suitable for a graduate or an advanced undergraduate course on game theory.

## An Introductory Course on Mathematical Game Theory

Author | : Julio González-Díaz,Ignacio García-Jurado,M. Gloria Fiestras-Janeiro |

Publsiher | : American Mathematical Society |

Total Pages | : 324 |

Release | : 2021-10-22 |

ISBN | : 1470465736 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**An Introductory Course on Mathematical Game Theory Book Excerpt:**

Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research. The book is suitable for a graduate or an advanced undergraduate course on game theory.

## Mathematical Foundations of Game Theory

Author | : Rida Laraki,Jérôme Renault,Sylvain Sorin |

Publsiher | : Springer Nature |

Total Pages | : 229 |

Release | : 2019-09-07 |

ISBN | : 303026646X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Mathematical Foundations of Game Theory Book Excerpt:**

This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text. Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.

## Game Theory

Author | : E. N. Barron |

Publsiher | : John Wiley & Sons |

Total Pages | : 574 |

Release | : 2013-04-22 |

ISBN | : 1118216938 |

Category | : Business & Economics |

Language | : EN, FR, DE, ES & NL |

**Game Theory Book Excerpt:**

An exciting new edition of the popular introduction to game theory and its applications The thoroughly expanded Second Edition presents a unique, hands-on approach to game theory. While most books on the subject are too abstract or too basic for mathematicians, Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models. With a rigorous, yet accessible, treatment of mathematics, the book focuses on results that can be used to determine optimal game strategies. Game Theory: An Introduction, Second Edition demonstrates how to use modern software, such as Maple™, Mathematica®, and Gambit, to create, analyze, and implement effective decision-making models. Coverage includes the main aspects of game theory including the fundamentals of two-person zero-sum games, cooperative games, and population games as well as a large number of examples from various fields, such as economics, transportation, warfare, asset distribution, political science, and biology. The Second Edition features: • A new chapter on extensive games, which greatly expands the implementation of available models • New sections on correlated equilibria and exact formulas for three-player cooperative games • Many updated topics including threats in bargaining games and evolutionary stable strategies • Solutions and methods used to solve all odd-numbered problems • A companion website containing the related Maple and Mathematica data sets and code A trusted and proven guide for students of mathematics and economics, Game Theory: An Introduction, Second Edition is also an excellent resource for researchers and practitioners in economics, finance, engineering, operations research, statistics, and computer science.

## Combinatorial Game Theory

Author | : Aaron N. Siegel |

Publsiher | : American Mathematical Soc. |

Total Pages | : 523 |

Release | : 2013-08-01 |

ISBN | : 082185190X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Combinatorial Game Theory Book Excerpt:**

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 Alive

Author | : Anna R. Karlin,Yuval Peres |

Publsiher | : American Mathematical Soc. |

Total Pages | : 372 |

Release | : 2017-04-27 |

ISBN | : 1470419823 |

Category | : Game theory |

Language | : EN, FR, DE, ES & NL |

**Game Theory Alive Book Excerpt:**

We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

## Cooperative Game Theory Tools in Coalitional Control Networks

Author | : Francisco Javier Muros |

Publsiher | : Springer |

Total Pages | : 218 |

Release | : 2019-04-24 |

ISBN | : 3030104893 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Cooperative Game Theory Tools in Coalitional Control Networks Book Excerpt:**

This book analyzes coalitional control schemes by incorporating concepts of cooperative game theory into a distributed control framework. It considers a networked architecture where the nodes are the agents and the edges are their communication links and either the agents or the links are established as the players of cooperative games related to the cost function of the coalitional schemes. The book discusses various cooperative game theory tools that are used to measure/analyze the players’ features, impose constraints on them, provide alternative methods of game computation, detect critical players inside the control scheme, and perform system partitioning of large-scale systems, such as the Barcelona drinking water network, which is described in a case study.

## Game Theory in Management Accounting

Author | : David Mueller,Ralf Trost |

Publsiher | : Springer |

Total Pages | : 450 |

Release | : 2017-09-21 |

ISBN | : 331961603X |

Category | : Business & Economics |

Language | : EN, FR, DE, ES & NL |

**Game Theory in Management Accounting Book Excerpt:**

This book demonstrates what kind of problems, originating in a management accounting setting, may be solved with game theoretic models. Game theory has experienced growing interest and numerous applications in the field of management accounting. The main focus traditionally has been on the field of non-cooperative behaviour, but the area of cooperative game theory has developed rapidly and has received increasing attention. Intensive research, in combination with the changing culture of publishing, has produced a nearly unmanageable number of publications in the areas concerned. Therefore, one main purpose of this volume is providing an intensive analysis of the intersection of these areas. In addition, the book strengthens the relationship between the theory and the practical applications and it illustrates the two-sided relationship between game theory and management accounting: new game theoretic models offer new fields of applications and these applications raise new questions for the theory.

## Game Theory

Author | : Andrew McEachern |

Publsiher | : Morgan & Claypool Publishers |

Total Pages | : 117 |

Release | : 2017-06-15 |

ISBN | : 1681731592 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Game Theory Book Excerpt:**

This book is a formalization of collected notes from an introductory game theory course taught at Queen's University. The course introduced traditional game theory and its formal analysis, but also moved to more modern approaches to game theory, providing a broad introduction to the current state of the discipline. Classical games, like the Prisoner's Dilemma and the Lady and the Tiger, are joined by a procedure for transforming mathematical games into card games. Included is an introduction and brief investigation into mathematical games, including combinatorial games such as Nim. The text examines techniques for creating tournaments, of the sort used in sports, and demonstrates how to obtain tournaments that are as fair as possible with regards to playing on courts. The tournaments are tested as in-class learning events, providing a novel curriculum item. Example tournaments are provided at the end of the book for instructors interested in running a tournament in their own classroom. The book is appropriate as a text or companion text for a one-semester course introducing the theory of games or for students who wish to get a sense of the scope and techniques of the field.

## An Introduction to Game Theoretic Modelling Third Edition

Author | : Mike Mesterton-Gibbons |

Publsiher | : American Mathematical Soc. |

Total Pages | : 395 |

Release | : 2019-07-05 |

ISBN | : 1470450291 |

Category | : Game theory |

Language | : EN, FR, DE, ES & NL |

**An Introduction to Game Theoretic Modelling Third Edition Book Excerpt:**

This book introduces game theory and its applications from an applied mathematician's perspective, systematically developing tools and concepts for game-theoretic modelling in the life and social sciences. Filled with down-to-earth examples of strategic behavior in humans and other animals, the book presents a unified account of the central ideas of both classical and evolutionary game theory. Unlike many books on game theory, which focus on mathematical and recreational aspects of the subject, this book emphasizes using games to answer questions of current scientific interest. In the present third edition, the author has added substantial new material on evolutionarily stable strategies and their use in behavioral ecology. The only prerequisites are calculus and some exposure to matrix algebra, probability, and differential equations.

## Pareto Nash Stackelberg Game and Control Theory

Author | : Valeriu Ungureanu |

Publsiher | : Springer |

Total Pages | : 343 |

Release | : 2018-03-09 |

ISBN | : 3319751514 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Pareto Nash Stackelberg Game and Control Theory Book Excerpt:**

This book presents a comprehensive new, multi-objective and integrative view on traditional game and control theories. Consisting of 15 chapters, it is divided into three parts covering noncooperative games; mixtures of simultaneous and sequential multi-objective games; and multi-agent control of Pareto-Nash-Stackelberg-type games respectively. Can multicriteria optimization, game theory and optimal control be integrated into a unique theory? Are there mathematical models and solution concepts that could constitute the basis of a new paradigm? Is there a common approach and method to solve emerging problems? The book addresses these and other related questions and problems to create the foundation for the Pareto-Nash-Stackelberg Game and Control Theory. It considers a series of simultaneous/Nash and sequential/Stackelberg games, single-criterion and multicriteria/Pareto games, combining Nash and Stackelberg game concepts and Pareto optimization, as well as a range of notions related to system control. In addition, it considers the problems of finding and representing the entire set of solutions. Intended for researches, professors, specialists, and students in the areas of game theory, operational research, applied mathematics, economics, computer science and engineering, it also serves as a textbook for various courses in these fields.

## Models for Cooperative Games with Fuzzy Relations among the Agents

Author | : Andrés Jiménez-Losada |

Publsiher | : Springer |

Total Pages | : 260 |

Release | : 2017-04-11 |

ISBN | : 3319564722 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Models for Cooperative Games with Fuzzy Relations among the Agents Book Excerpt:**

This book offers a comprehensive introduction to cooperative game theory and a practice-oriented reference guide to new models and tools for studying bilateral fuzzy relations among several agents or players. It introduces the reader to several fuzzy models, each of which is first analyzed in the context of classical games (crisp games) and subsequently in the context of fuzzy games. Special emphasis is given to the value of Shapley, which is presented for the first time in the context of fuzzy games. Students and researchers will find here a self-contained reference guide to cooperative fuzzy games, characterized by a wealth of examples, descriptions of a wide range of possible situations, step-by-step explanations of the basic mathematical concepts involved, and easy-to-follow information on axioms and properties.

## Systems of Systems Perspectives and Applications

Author | : Tien M. Nguyen |

Publsiher | : BoD – Books on Demand |

Total Pages | : 242 |

Release | : 2021-07-07 |

ISBN | : 1839683279 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Systems of Systems Perspectives and Applications Book Excerpt:**

This professional technical book presents complex topics on System-of-System (SoS) and Systems-of-Systems (SOS) engineering, SOS enterprise architecture (SOSEA) design and analysis, and implementation of SOSEA framework along with the modeling, simulation and analysis (MS&A) models in MATLAB. In addition, the book also extends the use of SOS perspectives for the development of computer simulation models for complex processes, systems, decision support systems, and game-theoretic models. This book is intended for two reader categories; namely, a primary and secondary category. The primary category includes system engineers, SOS architects, and mathematicians. The secondary category includes scientists and researchers in space/airborne systems, wireless communications, medicine, and mathematics, who would benefit from several chapters that contain open problems and technical relevance.

## Matt DeVos and Deborah A Kent

Author | : Matt DeVos,Deborah A. Kent |

Publsiher | : American Mathematical Soc. |

Total Pages | : 343 |

Release | : 2016-12-27 |

ISBN | : 1470422107 |

Category | : Combinatorial analysis |

Language | : EN, FR, DE, ES & NL |

**Matt DeVos and Deborah A Kent Book Excerpt:**

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.

## Operations Research and Enterprise Systems

Author | : Begoña Vitoriano,Greg H. Parlier |

Publsiher | : Springer |

Total Pages | : 261 |

Release | : 2017-02-14 |

ISBN | : 3319539825 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Operations Research and Enterprise Systems Book Excerpt:**

This book constitutes revised selected papers from the 5th International Conference on Operations Research and Enterprise Systems, ICORES 2016, held in Rome, Italy, in February 2016. The 14 papers presented in this volume were carefully reviewed and selection from a total of 75 submissions. They are organized in topical sections named: methodologies and technologies; and applications.

## Mathematical Game Theory

Author | : Ulrich Faigle |

Publsiher | : World Scientific |

Total Pages | : 240 |

Release | : 2022-02-25 |

ISBN | : 9811246718 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Mathematical Game Theory Book Excerpt:**

What is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly 'rational' human behavior in search of appropriate 'winning strategies'. This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle.This book takes a novel approach to the subject. Its focus is on mathematical models that apply to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably.This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples invite the reader to participate 'actively' when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.

## A First Course in Mathematical Economics

Author | : Sunanda Roy |

Publsiher | : Cambridge Scholars Publishing |

Total Pages | : 364 |

Release | : 2020-03-17 |

ISBN | : 1527548538 |

Category | : Business & Economics |

Language | : EN, FR, DE, ES & NL |

**A First Course in Mathematical Economics Book Excerpt:**

The book studies a set of mathematical tools and techniques most necessary for undergraduate economics majors as they transition from largely non-technical first-year principles courses into calculus-based upper-level courses in economics. The book’s presentation style places more emphasis on the intuition underlying the mathematical concepts and results discussed and less on proofs and technical details. Its discussion topics have been chosen in terms of their immediate usefulness for beginners, while examples and applications are drawn from material that is familiar from introductory economics courses.

## Solutions Manual for Games and Decision Making

Author | : Charalambos D. Aliprantis,Subir K. Chakrabarti |

Publsiher | : Unknown |

Total Pages | : 224 |

Release | : 2000 |

ISBN | : 9780195133691 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Solutions Manual for Games and Decision Making Book Excerpt:**

The authors are both mathematical economists; one teaches in an economics department and the other in a business school The latter is also editor of a prestigious economics journal and the author of 12 books in pure and applied mathematics. Because of their prestige as scholars and teachers, the National Science Foundation awarded them a grant to develop an interdisciplinary course, combining decision theory and game theory, for primary use in business and economics departments.The heart of business, and much of economics, is decision making. This book is a fully self-contained treatment of almost everything that can be called decision theory, from classical optimization, often covered in courses in mathematical economics and management science, to modern game theory, the cornerstone of modern managerial (micro) economics which provides the foundation for management strategy and competitive analysis. Only a knowledge of simple calculus and probability is required. Although some coverage in later chapters requires extra mathematical knowledge, that knowledge is developed as an integral part of the text. This book will be a key text for all professors who want to take a serious look at a decision theory, whether they are teaching undergraduate game theory or undergraduate or MBA courses in optimization and game theory.With careful selection of topics not to intimidate students, the authors show the integration of decision and game theory, as part of the same body of knowledge and demonstrates that unity. They move from the problem of the decision-maker, to progressively more complex decision problems, such as sequential rationality, culminating in topics of great immediate interest, auctions and bargaining. By building chapters squarely on what goes before, the authors avoid any unnecessary confusion in presenting a technical subject such as game theory, where ideas are often carelessly and callously presented out of proper sequence. The first chapter introduces optimization theory with a single decision-maker, by using problems from finance and business, to demonstrate how to find solutions to optimization problems. Building on concepts of the single decision-maker in the first chapter, Chapter 2 introduces fundamentals of modern game theory by developing the theory of strategic form games and their solutions, e.g. markets, voting auctions. Chapters 4 and 5 on sequential games builds on the foundation of Chapter 3 devoted to sequential decision-making. The concluding chapters (6&7) cover auctions and bargaining using what has preceded in Chapters 1-5.While the book is sound enough mathematically to be used in introductory mathematics courses on game theory, its broadest appeal will be in courses that show applications of decision theory in economics and business (perhaps even some political science courses at the graduate level). It has been successfully class tested in a management science course at the Krannert School of Management. The book shows the increasing importance of sound mathematical knowledge in decision-making for sustained competitive advantage.

## Psychometrika

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1960-03 |

ISBN | : 1928374650XXX |

Category | : Psychometrics |

Language | : EN, FR, DE, ES & NL |

**Psychometrika Book Excerpt:**

List of members of the society in v. 1, 4.

## A Gentle Introduction to Game Theory

Author | : Saul Stahl,American Mathematical Society |

Publsiher | : American Mathematical Soc. |

Total Pages | : 176 |

Release | : 1999 |

ISBN | : 0821813390 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**A Gentle Introduction to Game Theory Book Excerpt:**

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.