Download or read book An Introductory Course on Mathematical Game Theory written by Julio González-Díaz and published by American Mathematical Society. This book was released on 2021-10-22 with total page 324 pages. Available in PDF, EPUB and Kindle. 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.
Download or read book Mathematical Foundations of Game Theory written by Rida Laraki and published by Springer Nature. This book was released on 2019-09-07 with total page 240 pages. Available in PDF, EPUB and Kindle. 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.
Download or read book Game Theory and Strategy written by Philip D. Straffin and published by American Mathematical Society. This book was released on 2023-01-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to mathematical game theory, which might better be called the mathematical theory of conflict and cooperation. It is applicable whenever two individuals—or companies, or political parties, or nations—confront situations where the outcome for each depends on the behavior of all. What are the best strategies in such situations? If there are chances of cooperation, with whom should you cooperate, and how should you share the proceeds of cooperation? Since its creation by John von Neumann and Oskar Morgenstern in 1944, game theory has shed new light on business, politics, economics, social psychology, philosophy, and evolutionary biology. In this book, its fundamental ideas are developed with mathematics at the level of high school algebra and applied to many of these fields (see the table of contents). Ideas like “fairness” are presented via axioms that fair allocations should satisfy; thus the reader is introduced to axiomatic thinking as well as to mathematical modeling of actual situations.
Download or read book Mathematical Game Theory and Applications written by Vladimir Mazalov and published by John Wiley & Sons. This book was released on 2014-10-06 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Game Theory and Applications Mathematical Game Theory and Applications An authoritative and quantitative approach to modern game theory with applications from economics, political science, military science and finance. Mathematical Game Theory and Applications combines both the theoretical and mathematical foundations of game theory with a series of complex applications along with topics presented in a logical progression to achieve a unified presentation of research results. This book covers topics such as two-person games in strategic form, zero-sum games, N-person non-cooperative games in strategic form, two-person games in extensive form, parlor and sport games, bargaining theory, best-choice games, co-operative games and dynamic games. Several classical models used in economics are presented which include Cournot, Bertrand, Hotelling and Stackelberg as well as coverage of modern branches of game theory such as negotiation models, potential games, parlor games and best choice games. Mathematical Game Theory and Applications: Presents a good balance of both theoretical foundations and complex applications of game theory. Features an in-depth analysis of parlor and sport games, networking games, and bargaining models. Provides fundamental results in new branches of game theory, best choice games, network games and dynamic games. Presents numerous examples and exercises along with detailed solutions at the end of each chapter. Is supported by an accompanying website featuring course slides and lecture content. Covering a host of important topics, this book provides a research springboard for graduate students and a reference for researchers who might be working in the areas of applied mathematics, operations research, computer science or economical cybernetics.
Download or read book Games Theory and Applications written by L. C. Thomas and published by Courier Corporation. This book was released on 2012-12-13 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text opens with the theory of 2-person zero-sum games, 2-person non-zero sum games, and n-person games, at a level between non-mathematical introductory books and technical mathematical game theory books. Includes introductory explanations of gaming and meta games. Includes numerous exercises anbd problems with solutions and over 30 illustrations. 1986 edition.
Download or read book Game Theory written by A. J. Jones and published by Horwood Publishing. This book was released on 2000-12 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern, still relevant text is suitable for senior undergraduate and graduate students, teachers and professionals in mathematics, operational research, economics, sociology; and psychology, defence and strategic studies, and war games. Engagingly written with agreeable humor, the book can also be understood by non-mathematicians. It shows basic ideas of extensive form, pure and mixed strategies, the minimax theorem, non-cooperative and co-operative games, and a ''first class'' account of linear programming, theory and practice. The text is self-contained with comprehensive source references. Based on a series of lectures given by the author in the theory of games at Royal Holloway College, it gives unusually comprehensive but concise treatment of co-operative games, an original account of bargaining models, with a skilfully guided tour through the Shapely and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.
Download or read book Theory of Games and Statistical Decisions written by David A. Blackwell and published by Courier Corporation. This book was released on 2012-06-14 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory. The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games to normal forms, the minimax theorem, and the utility theorem. With this introduction, Blackwell and Professor Girshick look at: Values and Optimal Strategies in Games; General Structure of Statistical Games; Utility and Principles of Choice; Classes of Optimal Strategies; Fixed Sample-Size Games with Finite Ω and with Finite A; Sufficient Statistics and the Invariance Principle; Sequential Games; Bayes and Minimax Sequential Procedures; Estimation; and Comparison of Experiments. A few topics not directly applicable to statistics, such as perfect information theory, are also discussed. Prerequisites for full understanding of the procedures in this book include knowledge of elementary analysis, and some familiarity with matrices, determinants, and linear dependence. For purposes of formal development, only discrete distributions are used, though continuous distributions are employed as illustrations. The number and variety of problems presented will be welcomed by all students, computer experts, and others using statistics and game theory. This comprehensive and sophisticated introduction remains one of the strongest and most useful approaches to a field which today touches areas as diverse as gambling and particle physics.
Download or read book A Beautiful Math written by Tom Siegfried and published by National Academies Press. This book was released on 2006-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.
Download or read book Insights into Game Theory written by Ein-Ya Gura and published by Cambridge University Press. This book was released on 2008-11-13 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behaviour of competing individuals, firms and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only a basic understanding of mathematics. Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. The authors use four very different topics (college admission, social justice and majority voting, coalitions and co-operative games, and a bankruptcy problem from the Talmud) to investigate four areas of game theory. The result is a fascinating introduction to the world of game theory and its increasingly important role in the social sciences.
Download or read book Game Theory written by James N. Webb and published by Springer Science & Business Media. This book was released on 2007-03-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outstanding feature of this book is that it provides a unified account of three types of decision problem. It covers the basic ideas of decision theory, classical game theory, and evolutionary game theory in one volume. No background knowledge of economics or biology is required as examples have been carefully selected for their accessibility. Detailed solutions to the numerous exercises are provided at the back of the book, making it ideal for self-study. This introduction to game theory is intended as a first course for undergraduate students of mathematics, but it will also interest advanced students or researchers in biology and economics.
Download or read book Mathematical Methods of Game and Economic Theory written by Jean-Pierre Aubin and published by Courier Corporation. This book was released on 2007-01-01 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.
Download or read book Introduction to the Theory of Games written by J. C. C. McKinsey and published by Courier Corporation. This book was released on 2012-11-14 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive overview of the mathematical theory of games illustrates applications to situations involving conflicts of interest, including economic, social, political, and military contexts. Advanced calculus a prerequisite. Includes 51 figures and 8 tables. 1952 edition.
Download or read book N Person Game Theory written by Anatol Rapoport and published by Courier Corporation. This book was released on 2013-06-17 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVSequel to Two-Person Game Theory introduces necessary mathematical notation (mainly set theory), presents basic concepts and models, and provides applications to social situations. /div
Download or read book Introduction to Topology and Geometry written by Saul Stahl and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
Download or read book Two Person Game Theory written by Anatol Rapoport and published by Courier Corporation. This book was released on 2013-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Rock Paper Scissors written by Len Fisher and published by Basic Books. This book was released on 2008-11-04 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praised by Entertainment Weekly as “the man who put the fizz into physics,” Dr. Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.
Download or read book Game Theory written by Hans Peters and published by Springer. This book was released on 2015-06-04 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It is the second, revised version of the successful 2008 edition. The book covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book contains a problem section. Hints, answers and solutions are included.
