Foundations Of Game Theory

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Mathematical Foundations of Game Theory

Author : Rida Laraki
Publisher : Springer Nature
ISBN 13 : 303026646X
Total Pages : 240 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Mathematical Foundations of Game Theory by : Rida Laraki

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.

Game-Theoretic Foundations for Probability and Finance

Author : Glenn Shafer
Publisher : John Wiley & Sons
ISBN 13 : 1118547934
Total Pages : 483 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Game-Theoretic Foundations for Probability and Finance by : Glenn Shafer

Download or read book Game-Theoretic Foundations for Probability and Finance written by Glenn Shafer and published by John Wiley & Sons. This book was released on 2019-03-21 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Foundations of Non-cooperative Game Theory

Author : Klaus Ritzberger
Publisher : Oxford University Press on Demand
ISBN 13 : 9780199247851
Total Pages : 353 pages
Book Rating : 4.2/5 (478 download)

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Book Synopsis Foundations of Non-cooperative Game Theory by : Klaus Ritzberger

Download or read book Foundations of Non-cooperative Game Theory written by Klaus Ritzberger and published by Oxford University Press on Demand. This book was released on 2002 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a comprehensive overview of the main developments in game theory since the 1950s. It provides a wide variety of examples and exercises, mostly drawn from applications in economics, to illustrate key concepts and ideas in the field. The book should prove an invaluable reference tool for teachers, students, and researchers of microeconomics and game theory.

Game Theory

Author : Aviad Heifetz
Publisher : Cambridge University Press
ISBN 13 : 0521176042
Total Pages : 461 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Game Theory by : Aviad Heifetz

Download or read book Game Theory written by Aviad Heifetz and published by Cambridge University Press. This book was released on 2012-05-31 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the fundamentals of game theory for undergraduates and MBA students.

Two-Person Game Theory

Author : Anatol Rapoport
Publisher : Courier Corporation
ISBN 13 : 0486281094
Total Pages : 241 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Two-Person Game Theory by : Anatol Rapoport

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 241 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.

Epistemic Game Theory

Author : Andrés Perea
Publisher : Cambridge University Press
ISBN 13 : 1107008913
Total Pages : 581 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Epistemic Game Theory by : Andrés Perea

Download or read book Epistemic Game Theory written by Andrés Perea and published by Cambridge University Press. This book was released on 2012-06-07 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first textbook to explain the principles of epistemic game theory.

Game Theoretical Foundations of Evolutionary Stability

Author : Immanuel M. Bomze
Publisher : Springer Science & Business Media
ISBN 13 : 364245660X
Total Pages : 152 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Game Theoretical Foundations of Evolutionary Stability by : Immanuel M. Bomze

Download or read book Game Theoretical Foundations of Evolutionary Stability written by Immanuel M. Bomze and published by Springer Science & Business Media. This book was released on 2013-12-19 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes arose from discussions we had over a working paper written by the first author in fall 1987. We decided then to write a short paper about the basic structure of evolutionary stability and found ourselves ending up with a book manuscript. Parts of the material contained herein were presented in a seminar at the Department of Mathematics at the University of Vienna, as well as at a workshop on evolutionary game theory in Bielefeld. The final version of the manuscript has certainly benefitted from critical comments and suggestions by the participants of both the seminar and the workshop. Thanks are also due to S. Bomze-de Barba, R. Burger, G. Danninger, J. Hofbauer, R. Selten, K. Sigmund, G. Stiastny and F. Weising. The co-operation of W. Muller from Springer Verlag, Heidelberg, is gratefully acknowledged. Vienna, November 1988 Immanuel M. Bomze Benedikt M. Potscher III Contents 1. Introduction 1 2. Strategies and payoffs 5 2. 1. A general setting for evolutionary game theory 6 2. 2. Mixed strategies and population games 8 2. 3. Finite number of strategies . . . . . 13 2. 4. Infinitely many (pure) strategies 15 2. 5. Structured populations: asymmetric contests and multitype games 17 2. 6. Additional remarks . . . . . . . . . . . . . . . . . . . . . 21 3. Evolutionary stability 25 3. 1. Definition of evolutionary stability 25 3. 2. Evolutionary stability and solution concepts in classical game theory 30 3. 3. Conditions for evolutionary stability based on the normal cone 31 3. 4.

Game Theory

Author : Steve Tadelis
Publisher : Princeton University Press
ISBN 13 : 0691129088
Total Pages : 416 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Game Theory by : Steve Tadelis

Download or read book Game Theory written by Steve Tadelis and published by Princeton University Press. This book was released on 2013-01-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive introduction to game theory This comprehensive textbook introduces readers to the principal ideas and applications of game theory, in a style that combines rigor with accessibility. Steven Tadelis begins with a concise description of rational decision making, and goes on to discuss strategic and extensive form games with complete information, Bayesian games, and extensive form games with imperfect information. He covers a host of topics, including multistage and repeated games, bargaining theory, auctions, rent-seeking games, mechanism design, signaling games, reputation building, and information transmission games. Unlike other books on game theory, this one begins with the idea of rationality and explores its implications for multiperson decision problems through concepts like dominated strategies and rationalizability. Only then does it present the subject of Nash equilibrium and its derivatives. Game Theory is the ideal textbook for advanced undergraduate and beginning graduate students. Throughout, concepts and methods are explained using real-world examples backed by precise analytic material. The book features many important applications to economics and political science, as well as numerous exercises that focus on how to formalize informal situations and then analyze them. Introduces the core ideas and applications of game theory Covers static and dynamic games, with complete and incomplete information Features a variety of examples, applications, and exercises Topics include repeated games, bargaining, auctions, signaling, reputation, and information transmission Ideal for advanced undergraduate and beginning graduate students Complete solutions available to teachers and selected solutions available to students

An Introductory Course on Mathematical Game Theory

Author : Julio González-Díaz
Publisher : American Mathematical Society
ISBN 13 : 1470465736
Total Pages : 324 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introductory Course on Mathematical Game Theory by : Julio González-Díaz

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.

Game Theory

Author : Morton D. Davis
Publisher : Courier Corporation
ISBN 13 : 0486135152
Total Pages : 290 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Game Theory by : Morton D. Davis

Download or read book Game Theory written by Morton D. Davis and published by Courier Corporation. This book was released on 2012-05-11 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Twenty Lectures on Algorithmic Game Theory

Author : Tim Roughgarden
Publisher : Cambridge University Press
ISBN 13 : 1316781178
Total Pages : 356 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Twenty Lectures on Algorithmic Game Theory by : Tim Roughgarden

Download or read book Twenty Lectures on Algorithmic Game Theory written by Tim Roughgarden and published by Cambridge University Press. This book was released on 2016-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.

Essentials of Game Theory

Author : Kevin Gebser
Publisher : Springer Nature
ISBN 13 : 3031015452
Total Pages : 88 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Essentials of Game Theory by : Kevin Gebser

Download or read book Essentials of Game Theory written by Kevin Gebser and published by Springer Nature. This book was released on 2022-05-31 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory is the mathematical study of interaction among independent, self-interested agents. The audience for game theory has grown dramatically in recent years, and now spans disciplines as diverse as political science, biology, psychology, economics, linguistics, sociology, and computer science, among others. What has been missing is a relatively short introduction to the field covering the common basis that anyone with a professional interest in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This Synthesis Lecture aims to fill this gap by providing a concise and accessible introduction to the field. It covers the main classes of games, their representations, and the main concepts used to analyze them.

Theory of Games and Statistical Decisions

Author : David A. Blackwell
Publisher : Courier Corporation
ISBN 13 : 0486150895
Total Pages : 388 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Theory of Games and Statistical Decisions by : David A. Blackwell

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.

Game Theory with Engineering Applications

Author : Dario Bauso
Publisher : SIAM
ISBN 13 : 1611974275
Total Pages : 298 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Game Theory with Engineering Applications by : Dario Bauso

Download or read book Game Theory with Engineering Applications written by Dario Bauso and published by SIAM. This book was released on 2016-02-29 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems are highly distributed collective systems that have humans in the loop. Engineering systems emphasize the potential of control and games beyond traditional applications. Game theory can be used to design incentives to obtain socially desirable behaviors on the part of the players, for example, a change in the consumption patterns on the part of the ?prosumers? (producers-consumers) or better redistribution of traffic. This unique book addresses the foundations of game theory, with an emphasis on the physical intuition behind the concepts, an analysis of design techniques, and a discussion of new trends in the study of cooperation and competition in large complex distributed systems.?

A Course on Cooperative Game Theory

Author : Satya R. Chakravarty
Publisher : Cambridge University Press
ISBN 13 : 1107058791
Total Pages : 277 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis A Course on Cooperative Game Theory by : Satya R. Chakravarty

Download or read book A Course on Cooperative Game Theory written by Satya R. Chakravarty and published by Cambridge University Press. This book was released on 2015-02-09 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Deals with real life situations where objectives of the participants are partially cooperative and partially conflicting"--

Classics in Game Theory

Author : Harold William Kuhn
Publisher : Princeton University Press
ISBN 13 : 1400829151
Total Pages : 328 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Classics in Game Theory by : Harold William Kuhn

Download or read book Classics in Game Theory written by Harold William Kuhn and published by Princeton University Press. This book was released on 2020-11-10 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classics in Game Theory assembles in one sourcebook the basic contributions to the field that followed on the publication of Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern (Princeton, 1944). The theory of games, first given a rigorous formulation by von Neumann in a in 1928, is a subfield of mathematics and economics that models situations in which individuals compete and cooperate with each other. In the "heroic era" of research that began in the late 1940s, the foundations of the current theory were laid; it is these fundamental contributions that are collected in this volume. In the last fifteen years, game theory has become the dominant model in economic theory and has made significant contributions to political science, biology, and international security studies. The central role of game theory in economic theory was recognized by the award of the Nobel Memorial Prize in Economic Science in 1994 to the pioneering game theorists John C. Harsanyi, John Nash, and Reinhard Selten. The fundamental works for which they were honored are all included in this volume. Harold Kuhn, himself a major contributor to game theory for his reformulation of extensive games, has chosen eighteen essays that constitute the core of game theory as it exists today. Drawn from a variety of sources, they will be an invaluable tool for researchers in game theory and for a broad group of students of economics, political science, and biology.

Repeated Games

Author : Jean-François Mertens
Publisher : Cambridge University Press
ISBN 13 : 110703020X
Total Pages : 597 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Repeated Games by : Jean-François Mertens

Download or read book Repeated Games written by Jean-François Mertens and published by Cambridge University Press. This book was released on 2015-02-09 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This landmark work significantly advances the literature on game theory with a masterful conceptual presentation of the CORE working papers published in 1994.