Mathematical Foundations Of Game Theory
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| Author | : Rida Laraki |
| Publisher | : Springer Nature |
| Total Pages | : 240 |
| Release | : 2019-09-07 |
| Genre | : Mathematics |
| ISBN | : 303026646X |
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.
| Author | : Julio González-Díaz |
| Publisher | : American Mathematical Society |
| Total Pages | : 324 |
| Release | : 2021-10-22 |
| Genre | : Mathematics |
| ISBN | : 1470465736 |
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.
| Author | : Anatol Rapoport |
| Publisher | : Courier Corporation |
| Total Pages | : 241 |
| Release | : 2013-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486281094 |
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.
| Author | : Glenn Shafer |
| Publisher | : John Wiley & Sons |
| Total Pages | : 483 |
| Release | : 2019-03-21 |
| Genre | : Business & Economics |
| ISBN | : 1118547934 |
Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University
| 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 | : James N. Webb |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 237 |
| Release | : 2007-03-06 |
| Genre | : Mathematics |
| ISBN | : 1846286360 |
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.
| Author | : Morton D. Davis |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2012-05-11 |
| Genre | : Mathematics |
| ISBN | : 0486135152 |
This fascinating, newly revised edition offers an overview of game theory, plus lucid coverage of two-person zero-sum game with equilibrium points; general, two-person zero-sum game; utility theory; and other topics.
| Author | : Pierre Bernhard |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 348 |
| Release | : 2012-12-14 |
| Genre | : Mathematics |
| ISBN | : 0817683887 |
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods. A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including: · probability-free Black-Scholes theory; · fair-price interval of an option; · representation formulas and fast algorithms for option pricing; · rainbow options; · tychastic approach of mathematical finance based upon viability theory. This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.
| Author | : Avner Friedman |
| Publisher | : Courier Corporation |
| Total Pages | : 372 |
| Release | : 2013-06-06 |
| Genre | : Mathematics |
| ISBN | : 0486153274 |
Graduate-level text surveys games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, games with restricted phase coordinates, and N-person games. 1971 edition.
| Author | : Dario Bauso |
| Publisher | : Now Publishers |
| Total Pages | : 166 |
| Release | : 2014-10-06 |
| Genre | : Mathematics |
| ISBN | : 9781601989086 |
This is the first tutorial to give such a concise and accessible introduction to game theory. It will be of use to all students, practitioners, and researchers looking to understand the basic concepts, models, and applications.
