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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.
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.
This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning. Designed as a textbook for an undergraduate mathematics class and with ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the generous sets of exercises at various levels.
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
This modern, still relevant text is suitable for senior undergraduate and graduate students, teachers and professionals in mathematics, operational research, economics, sociology; and psychology, defence and strategic studies, and war games. Engagingly written with agreeable humor, the book can also be understood by non-mathematicians. It shows basic ideas of extensive form, pure and mixed strategies, the minimax theorem, non-cooperative and co-operative games, and a ''first class'' account of linear programming, theory and practice. The text is self-contained with comprehensive source references. Based on a series of lectures given by the author in the theory of games at Royal Holloway College, it gives unusually comprehensive but concise treatment of co-operative games, an original account of bargaining models, with a skilfully guided tour through the Shapely and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.
Designed primarily for economists and those interested in management economics who are not necessarily accomplished mathematicians, this text offers a clear, concise exposition of the relationship of linear programming to standard economic analysis. The research and writing were supported by The RAND Corporation in the late 1950s. Linear programming has been one of the most important postwar developments in economic theory, but until publication of the present volume, no text offered a comprehensive treatment of the many facets of the relationship of linear programming to traditional economic theory. This book was the first to provide a wide-ranging survey of such important aspects of the topic as the interrelations between the celebrated von Neumann theory of games and linear programming, and the relationship between game theory and the traditional economic theories of duopoly and bilateral monopoly. Modern economists will especially appreciate the treatment of the connection between linear programming and modern welfare economics and the insights that linear programming gives into the determinateness of Walrasian equilibrium. The book also offers an excellent introduction to the important Leontief theory of input-output as well as extensive treatment of the problems of dynamic linear programming. Successfully used for three decades in graduate economics courses, this book stresses practical problems and specifies important concrete applications.
Simple exposition of linear programming and matrix games covers convex sets in the Cartesian plane and the fundamental extreme point theorem for convex polygons; the simplex method in linear programming; the fundamental duality theorem and its corollary, von Neumann's minimax theorem; more. Easily understood problems and illustrative exercises. 1963 edition.
This book on constrained optimization is novel in that it fuses these themes: • use examples to introduce general ideas; • engage the student in spreadsheet computation; • survey the uses of constrained optimization;. • investigate game theory and nonlinear optimization, • link the subject to economic reasoning, and • present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the student’s interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the student’s grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics.
The mathematical study of games is an intriguing endeavor with implications and applications that reach far beyond tic-tac-toe, chess, and poker to economics, business, and even biology and politics. Most texts on the subject, however, are written at the graduate level for those with strong mathematics, economics, or business backgrounds. In