Topics In Mathematical Economics And Game Theory
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Topics In Mathematical Economics And Game Theory
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Author : Robert J. Aumann
language : en
Publisher:
Release Date : 1999
Topics In Mathematical Economics And Game Theory written by Robert J. Aumann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Economics, Mathematical categories.
Mathematical Methods Of Game And Economic Theory
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Author : Jean-Pierre Aubin
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Mathematical Methods Of Game And Economic Theory written by Jean-Pierre Aubin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
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.
Topics In Mathematical Economics And Game Theory
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Author : Robert J. Aumann
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Topics In Mathematical Economics And Game Theory written by Robert J. Aumann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Business & Economics categories.
Among his contributions to game theory, economics, and mathematics, Aumann introduced the concept of "acceptable points." As this endeared him to many game theorists, a reprint of his seminal 1959 paper on "Acceptable Points in General Cooperative n-Person Games" leads the 17 offerings on cooperative and non-cooperative game theory and economics and social choice. A number of these papers or related works were presented at the Fields Institute Conference, "New Directions in the Theory of Markets and Games," held October 1995 in Toronto honoring Aumann. The conference program concludes the text. Lacks an index. Annotation copyrighted by Book News, Inc., Portland, OR
Mathematical Foundations Of Game Theory
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Author : Rida Laraki
language : en
Publisher: Springer Nature
Release Date : 2019-09-07
Mathematical Foundations Of Game Theory written by Rida Laraki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-07 with Mathematics categories.
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
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Author : Hans Peters
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-15
Game Theory written by Hans Peters and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-15 with Business & Economics categories.
This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers topics of interest in game theory, including cooperative game theory. Every chapter includes a problem section.
Fixed Points And Economic Equilibria
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Author : Ken Urai
language : en
Publisher: World Scientific
Release Date : 2010-05-13
Fixed Points And Economic Equilibria written by Ken Urai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-13 with Mathematics categories.
This book presents a systematic approach to problems in economic equilibrium based on fixed-point arguments and rigorous set-theoretical (axiomatic) methods. It describes the highest-level research on the classical theme, fixed points and economic equilibria, in the theory of mathematical economics, and also presents basic results in this area, especially in the general equilibrium theory and non-co-operative game theory. The arguments also contain distinguishable developments of the main theme in the homology theory for general topological spaces, in the model theory and mathematical logic, and in the methodology and philosophy of social sciences. It can thus serve as a graduate-level textbook on mathematical economics as well as an advanced monograph for students and researchers who are concerned about rigorous mathematical treatment in the social sciences.
Game Theory
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Author : James N. Webb
language : en
Publisher: Springer Verlag
Release Date : 2007
Game Theory written by James N. Webb and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Business & Economics categories.
This introduction to game theory is written from a mathematical perspective. Its primary purpose is to be a first course for undergraduate students of mathematics, but it also contains material which will be of interest to advanced students or researchers in biology and economics. The outstanding feature of the book is that it provides a unified account of three types of decision problem: Situations involving a single decision-maker: in which a sequence of choices is to be made in "a game against nature". This introduces the basic ideas of optimality and decision processes. Classical game theory: in which the interactions of two or more decision-makers are considered. This leads to the concept of the Nash equilibrium. Evolutionary game theory: in which the changing structure of a population of interacting decision makers is considered. This leads to the ideas of evolutionarily stable strategies and replicator dynamics. An understanding of basic calculus and probability is assumed but no prior knowledge of game theory is required. Detailed solutions are provided for the numerous exercises.
Game Theory
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Author : Aviad Heifetz
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-31
Game Theory written by Aviad Heifetz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-31 with Business & Economics categories.
A guide to the fundamentals of game theory for undergraduates and MBA students.
Discrete Mathematics And Game Theory
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Author : Guillermo Owen
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-11-30
Discrete Mathematics And Game Theory written by Guillermo Owen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-30 with Business & Economics categories.
This book describes highly applicable mathematics without using calculus or limits in general. The study agrees with the opinion that the traditional calculus/analysis is not necessarily the only proper grounding for academics who wish to apply mathematics. The choice of topics is based on a desire to present those facets of mathematics which will be useful to economists and social/behavioral scientists. The volume is divided into seven chapters. Chapter I presents a brief review of the solution of systems of linear equations by the use of matrices. Chapter III introduces the theory of probability. The rest of the book deals with new developments in mathematics such as linear and dynamic programming, the theory of networks and the theory of games. These developments are generally recognized as the most important field in the `new mathematics' and they also have specific applications in the management sciences.
Fundamentals Of General Equilibrium Analysis
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Author : Takashi Suzuki
language : en
Publisher: World Scientific
Release Date : 2020-09-03
Fundamentals Of General Equilibrium Analysis written by Takashi Suzuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-03 with Business & Economics categories.
The aim of this book is to incorporate Marshallian ideas such as external increasing returns and monopolistic competitions into the general equilibrium framework of Walrasian tradition. New chapters and sections have been added to this revised and expanded edition of General Equilibrium Analysis of Production and Increasing Returns (World Scientific, 2009).The new material includes a presentation of equilibrium existence and core equivalence theorems for an infinite horizon economy with a measure space of consumers. These results are currently the focus of extensive studies by mathematical theorists, and are obtained by an application of an advanced mathematical concept called saturated (super-atomless) measure space.The second major change is the inclusion of a simple toy model of a liberal society which implements the difference principle proposed by J Rawls as a principle of distributive justice. This new section opens up a possibility to connect theoretical economics and political philosophy.Thirdly, the author presents the marginal cost pricing equilibrium and discusses welfare properties of the external increasing returns, which also belong to Marshall/ Pigou tradition of the Cambridge school.Finally, a new mathematical appendix treats basics of singular homology theory. Although the fixed point theorem is originally a theorem of algebraic topology, most economic students know its proof only in the context of the differentiable manifold theory presented by J Milnor. Considering the significance of the fixed point theorem and its playing a key role in general equilibrium theory, the purpose of this new appendix is to provide readers with the idea of a proof of Brower's fixed point theorem from the 'right place'.This volume will be helpful for graduate students and researchers of mathematical economics, game theory, and microeconomics.