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Author: Samuel Karlin
Publisher: Elsevier
ISBN: 1483222985
Category : Mathematics
Languages : en
Pages : 444
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Book Description
Matrix Games, Programming, and Mathematical Economics deals with game theory, programming theory, and techniques of mathematical economics in a single systematic theory. The principles of game theory and programming are applied to simplified problems related to economic models, business decisions, and military tactics. The book explains the theory of matrix games and some of the tools used in the analysis of matrix games. The text describes optimal strategies for matrix games which have two basic properties, as well as the construction of optimal strategies. The book investigates the structure of sets of solutions of discrete matrix games, with emphasis on the class of games whose solutions are unique. The examples show the use of dominance concepts, symmetries, and probabilistic arguments that emphasize the principles of game theory. One example involves two opposing political parties in an election campaign, particularly, how they should distribute their advertising efforts for wider exposure. The text also investigates how to determine an optimal program from several choices that results with the maximum or minimum objective. The book also explores the analogs of the duality theorem, the equivalence of game problems to linear programming problems, and also the inter-industry nonlinear activity analysis model requiring special mathematical methods. The text will prove helpful for students in advanced mathematics and calculus. It can be appreciated by mathematicians, engineers, economists, military strategists, or statisticians who formulate decisions using mathematical analysis and linear programming.
Author: Samuel Karlin
Publisher: Elsevier
ISBN: 1483222985
Category : Mathematics
Languages : en
Pages : 444
Get Book Here
Book Description
Matrix Games, Programming, and Mathematical Economics deals with game theory, programming theory, and techniques of mathematical economics in a single systematic theory. The principles of game theory and programming are applied to simplified problems related to economic models, business decisions, and military tactics. The book explains the theory of matrix games and some of the tools used in the analysis of matrix games. The text describes optimal strategies for matrix games which have two basic properties, as well as the construction of optimal strategies. The book investigates the structure of sets of solutions of discrete matrix games, with emphasis on the class of games whose solutions are unique. The examples show the use of dominance concepts, symmetries, and probabilistic arguments that emphasize the principles of game theory. One example involves two opposing political parties in an election campaign, particularly, how they should distribute their advertising efforts for wider exposure. The text also investigates how to determine an optimal program from several choices that results with the maximum or minimum objective. The book also explores the analogs of the duality theorem, the equivalence of game problems to linear programming problems, and also the inter-industry nonlinear activity analysis model requiring special mathematical methods. The text will prove helpful for students in advanced mathematics and calculus. It can be appreciated by mathematicians, engineers, economists, military strategists, or statisticians who formulate decisions using mathematical analysis and linear programming.
Author: Samuel Karlin
Publisher:
ISBN:
Category : Economics, Mathematical
Languages : en
Pages : 408
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Book Description
V. 1 : Matrix games, programming, and mathematical economics. v. 2 : The theory of infinite games.
Author: Angel de la Fuente
Publisher: Cambridge University Press
ISBN: 9780521585293
Category : Business & Economics
Languages : en
Pages : 630
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Book Description
A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.
Author: Paul R. Thie
Publisher: John Wiley & Sons
ISBN: 1118165454
Category : Mathematics
Languages : en
Pages : 476
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Book Description
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: Samuel Karlin
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Jean-Pierre Aubin
Publisher: Courier Corporation
ISBN: 048646265X
Category : Mathematics
Languages : en
Pages : 658
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Book Description
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.
Author: Samuel Karlin
Publisher: Elsevier
ISBN: 1483224007
Category : Mathematics
Languages : en
Pages : 399
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Book Description
Mathematical Methods and Theory in Games, Programming, and Economics, Volume II provides information pertinent to the mathematical theory of games of strategy. This book presents the mathematical tools for manipulating and analyzing large sets of strategies. Organized into nine chapters, this volume begins with an overview of the fundamental concepts in game theory, namely, strategy and pay-off. This text then examines the identification of strategies with points in Euclidean n-space, which is a convenience that simplifies the mathematical analysis. Other chapters provide a discussion of the theory of finite convex games. This book discusses as well the extension of the theory of convex continuous games to generalized convex games, which leads to the characterization that such games possess optimal strategies of finite type. The final chapter deals with the components of a simple two-person poker game. This book is a valuable resource for mathematicians, statisticians, economists, social scientists, and research workers.
Author: Akira Takayama
Publisher: Cambridge University Press
ISBN: 9780521314985
Category : Business & Economics
Languages : en
Pages : 770
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Book Description
This systematic exposition and survey of mathematical economics emphasizes the unifying structures of economic theory.
Author: John B. Guerard, Jr.
Publisher: Springer Science & Business Media
ISBN: 0387774394
Category : Business & Economics
Languages : en
Pages : 796
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Book Description
Portfolio construction is fundamental to the investment management process. In the 1950s, Harry Markowitz demonstrated the benefits of efficient diversification by formulating a mathematical program for generating the "efficient frontier" to summarize optimal trade-offs between expected return and risk. The Markowitz framework continues to be used as a basis for both practical portfolio construction and emerging research in financial economics. Such concepts as the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT), for example, provide the foundation for setting benchmarks, for predicting returns and risk, and for performance measurement. This volume showcases original essays by some of today’s most prominent academics and practitioners in the field on the contemporary application of Markowitz techniques. Covering a wide spectrum of topics, including portfolio selection, data mining tests, and multi-factor risk models, the book presents a comprehensive approach to portfolio construction tools, models, frameworks, and analyses, with both practical and theoretical implications.
Author: Thomas L., Saaty
Publisher: RWS Publications
ISBN: 1888603380
Category : Business & Economics
Languages : en
Pages : 404
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Book Description
"We are surrounded and deeply involved, in the natural world, with non- linear events which are not necessarily mathematical," the authors write. "For example . . . the nonlinear problem of pedalling a bicycle up and down a hillside. On a grand scale . . . the struggle for existence between two species, one of which preys exclusively on the other." This book is' for mathematicians and researchers who believe that "nonlinear mathematics is' the mathematics of today"; it is also for economists, engineers, operations analysts, "the reader who has been thus bemused into an artificially linear conception of the universe." Nonlinear Mathematics is the first attempt to consider the widest range of nonlinear topics found in the -scattered literature. Accessible to non- mathematics professionals as well as college seniors and graduates, it offers a discussion both particular and broad enough to stimulate research towards a unifying theory of nonlinear mathematics. Ideas are presented "according to existence and uniqueness theorems, characterization (e.g., stability and asymptotic behavior), construction of solutions, convergence, approximation and errors."
