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| Author | : Harold William Kuhn |
| Publisher | : Princeton University Press |
| Total Pages | : 224 |
| Release | : 1950-12-21 |
| Genre | : Mathematics |
| ISBN | : 9780691079349 |
The description for this book, Contributions to the Theory of Games (AM-24), Volume I, will be forthcoming.
| Author | : Elliott Mendelson |
| Publisher | : CRC Press |
| Total Pages | : 342 |
| Release | : 2024-08-02 |
| Genre | : Mathematics |
| ISBN | : 104009189X |
This classic text, originally from the noted logician Elliot Mendelson, is intended to be an easy-to-read introduction to the basic ideas and techniques of game theory. It can be used as a class textbook or for self-study. Introducing Game Theory and its Applications, Second Edition presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the authors begin with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solutions. Here the authors present the simplex method based on linear programming for solving these games and develop within this presentation the required background. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory. The book is suitable for a first undergraduate course in game theory, or a graduate course for students with limited previous exposure. It is useful for students who need to learn some game theory for a related subject (e.g., microeconomics) and have a limited mathematical background. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences. The authors hope this book breeds curiosity about the subject as its design is meant to to satisfy the readers. The book will prepare readers for deeper study of game theory applications in many fields of study.
| Author | : John Von Neumann |
| Publisher | : Diana |
| Total Pages | : 660 |
| Release | : 2020-01-29 |
| Genre | : Games & Activities |
| ISBN | : 9785608789779 |
This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.
| Author | : Anna R. Karlin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 400 |
| Release | : 2017-04-27 |
| Genre | : Mathematics |
| ISBN | : 1470419823 |
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.
| Author | : Robert J. Aumann |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 0 |
| Release | : 2024-01-28 |
| Genre | : Business & Economics |
| ISBN | : 9789811221064 |
Robert Aumann was awarded (jointly with Thomas C Schelling) the 2005 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 'for having enhanced our understanding of conflict and cooperation through game-theory analysis'. This book contains ten of his most important contributions to game theory, as selected by Eric Maskin, also a Nobel laureate.
| Author | : Harold William Kuhn |
| Publisher | : Princeton University Press |
| Total Pages | : 408 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400881978 |
These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
| Author | : Paul R. Thie |
| Publisher | : John Wiley & Sons |
| Total Pages | : 476 |
| Release | : 2011-09-15 |
| Genre | : Mathematics |
| ISBN | : 1118165454 |
Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.
| Author | : David A. Blackwell |
| Publisher | : Courier Corporation |
| Total Pages | : 388 |
| Release | : 2012-06-14 |
| Genre | : Mathematics |
| ISBN | : 0486150895 |
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.
| Author | : Michael Maschler |
| Publisher | : Cambridge University Press |
| Total Pages | : 1053 |
| Release | : 2020-06-25 |
| Genre | : Business & Economics |
| ISBN | : 1108493459 |
This new edition is unparalleled in breadth of coverage, thoroughness of technical explanations and number of worked examples.
| Author | : Matthew P. Goodman |
| Publisher | : Rowman & Littlefield |
| Total Pages | : 84 |
| Release | : 2019-11-08 |
| Genre | : Political Science |
| ISBN | : 1442281375 |
As the United States and China mark their 40th anniversary of formal diplomatic relations in 2019, the world’s most important bilateral relationship is increasingly defined by mistrust, competition, and uncertainty. After four decades of deepening economic integration, the talk in Washington today is about the extent to which the two economies will “decouple” over the years ahead. We drew on several different academic disciplines to help us model how an economic conflict between the United States and China could escalate and eventually de-escalate. Despite the challenges inherent in modelling economic conflict, our model was validated to a surprising extent by both our simulations and real-world developments. The project produced several findings that were both unexpected and relevant to policy, including that economic conflict is likely to be an enduring feature of the U.S.-China relationship for many years to come. Until perceptions of relative costs in the two countries shift, Washington and Beijing seem set on a path of continued escalation, no substantial trade deal, and at least partial decoupling of their economies. Reflecting on these findings, the report also provides recommendations for U.S. policymakers seeking to engage in successful economic bargaining with China.
