Author : Samuel Karlin
Publisher :
Page : 408 pages
File Size : 22,67 MB
Release : 1959
Category : Economics, Mathematical
ISBN :
V. 1 : Matrix games, programming, and mathematical economics. v. 2 : The theory of infinite games.
Author : Samuel Karlin
Publisher : Elsevier
Page : 444 pages
File Size : 50,43 MB
Release : 2014-05-12
Category : Mathematics
ISBN : 1483222985
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
Page : 399 pages
File Size : 50,77 MB
Release : 2014-05-12
Category : Mathematics
ISBN : 1483224007
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 : Angel de la Fuente
Publisher : Cambridge University Press
Page : 630 pages
File Size : 37,56 MB
Release : 2000-01-28
Category : Business & Economics
ISBN : 9780521585293
A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.
Author : Samuel Karlin
Publisher :
Page : 408 pages
File Size : 15,82 MB
Release : 1959
Category : Economics, Mathematical
ISBN :
Author : Samuel Karlin
Publisher :
Page : 454 pages
File Size : 27,47 MB
Release : 1959
Category : Economics, Mathematical
ISBN :
Author : Jean-Pierre Aubin
Publisher : Courier Corporation
Page : 658 pages
File Size : 26,56 MB
Release : 2007-01-01
Category : Mathematics
ISBN : 048646265X
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 : Paul R. Thie
Publisher : John Wiley & Sons
Page : 476 pages
File Size : 27,53 MB
Release : 2011-09-15
Category : 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 : Michael D. Intriligator
Publisher : SIAM
Page : 515 pages
File Size : 27,37 MB
Release : 2002-01-01
Category : Mathematics
ISBN : 0898715113
A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.
Author : Louis Brickman
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 17,88 MB
Release : 2012-12-06
Category : Business & Economics
ISBN : 1461245400
Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableau, minimal in size and notation, are employed for the simplex algorithm. In the context of these tableau the beautiful termination theorem of R.G. Bland is proven more simply than heretofore, and the important duality theorem becomes almost obvious. Examples and extensive discussions throughout the book provide insight into definitions, theorems, and applications. There is considerable informal discussion on how best to play matrix games. The book is designed for a one-semester undergraduate course. Readers will need a degree of mathematical sophistication and general tools such as sets, functions, and summation notation. No single college course is a prerequisite, but most students will do better with some prior college mathematics. This thorough introduction to linear programming and game theory will impart a deep understanding of the material and also increase the student's mathematical maturity.
