Book Description

This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed.Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students. ... Read more

Book Description

This book offers an in-depth overview of polyhedral methods and efficient algorithms in combinatorial optimization.These methods form a broad, coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science. In eight parts, various areas are treated, each starting with an elementary introduction to the area, with short, elegant proofs of the principal results, and each evolving to the more advanced methods and results, with full proofs of some of the deepest theorems in the area. Over 4000 references to further research are given, and historical surveys on the basic subjects are presented. ... Read more

Reviews (1)

A encyclopaedic reference on combinatorial optimization
A definitive account of the history and present state of combinatorial optimization from an author who is one of the most respected researchers in this area. The author has won the Dantzig award, the Fulkerson prize (twice) and the Lanchester Prize for his earlier classic text on "Theory of Linear and Integer Programming". Given the current pricing, it is a steal with over 1800 pages spread across three volumes. This is certainly not a text to be read from cover to cover but is a handy reference if you are interested in combinatorial optimization as a research topic or in the related areas of optimization, integer programming, polyhedral combinatorics, or graph theory.

The author gives short and elegants proof of most of the results. The reader is expected to have a background in graph theory, linear programming and integer programming. The author cites some results without proofs from his earlier books , "Theory of Linear and Integer Programming", and "Geometric Algorithms and Combinatorial Optimization". The book does not concentrate on applications and modeling aspects of combinatorial optimization problems and it does not dwell on the computational methods for NP-hard problems. The book does not offer exercises but lists some open problems and research topics (updated on author's website).

The book is mainly devoted to the theoretical developments in this field. Quoting the author, "We aim at offering an introduction and an in-depth survey of polyhedral combinatorics and efficient algorithms ... In the astonishing event that NP=P will be proved, this book will be highly incomplete". The results in this book are up to date till 2002 (updates are available at the author's website). In short this book should be invaluable for a graduate student or a researcher. ... Read more

Book Description

Decision makers in many areas, from industry to engineering and the social sector, face an increasing need to consider multiple, conflicting objectives in their decision processes. In many cases these real world decision problems can be formulated as multicriteria mathematical optimization models. The solution of such models requires appropriate techniques to compute so called efficient, or Pareto optimal, or compromise solutions that - unlike traditional mathematical programming methods - take the contradictory nature of the criteria into account. This book provides the necessary mathematical foundation of multicriteria optimization to solve nonlinear, linear and combinatorial problems with multiple criteria. Motivational examples illustrate the use of multicriteria optimization in practice. Numerous illustrations and exercises as well as an extensive bibliography are provided.

In the new edition a chapter on optimality conditions has been added. The linear programming part has been extended and includes new developments. Moreover, motivational examples are now introducing the majority of chapters.

Reviews (1)

The best book for a serious game theorist
I was looking for a reference material on Nash equilibrium in non-cooperative n-person games and this is the best book available. A must have for any game theorist: simply written and comprehensive. ... Read more

Book Description

Game theory is a key element in most decision making processes involving two or more people or organizations. This book explains how game theory can predict the outcome of complex decision making processes, and how it can help to improve negotiation and decision-making skills. It is grounded in well-established theory, yet the wide-ranging international examples used to illustrate its application offer a fresh approach to what is becoming an essential weapon in the armory of the informed manager. The book is accessibly written, explaining in simple terms the underlying mathematics behind games of skill. It analyzes more sophisticated topics such as zero-sum games, mixed-motive games, and multi-person games, coalitions and power. Clear examples and helpful diagrams are used throughout, and the mathematics is kept to a minimum. Written for managers, students and decision-makers in every field. ... Read more

Reviews (1)

A Solid Effort!
Anthony Kelly's book will help you take a step back from the day-to-day fray, and be more strategic in your approach to solving problems. He explains that during conflicts, people operate in their own perceived best interests. Sometimes, combatants can find a common ground, but sometimes the conflict is a "zero-sum game," with a winner and a loser. To come out on top as a player or manager, take advantage of the approaches and concepts of game theory. A word of caution, this volume relies heavily on formulas and decision-trees that may be beyond the ready grasp of non-technically minded managers. For those who want to put emotion aside and think strategically, however, reading this book is a rational move. We recommend it to those with mathematical or analytical skills, and finds that it will prove useful even to non-analysts who want to learn the fundamental concepts of game theory. ... Read more

Book Description

Since the first edition was published, computers have become ever more powerful, design engineers are tackling more complex systems, and the term "optimization" is now routinely used to denote a design process with increased speed and quality. This second edition takes account of these developments and brings the original text thoroughly up to date.The book now discusses trust region and convex approximation algorithms.A new chapter focuses on how to construct optimal design models.Three new case studies illustrate the creation of optimization models.The final chapter on optimization practice has been expanded to include computation of derivatives, interpretation of algorithmic results, and selection of algorithms and software. ... Read more

Book Description

Reviews (2)

More Bush-bashing than Biology
Barash's book provides a highly readable, basic, non-mathematical overview of the primary games, focusing on prisoner's dilemma and chicken although others are covered. I bought the book because of its advertised emphasis on applying game theory to biology and the animal kingdom. Unfortunately, too often the book simply serves to showcase Barash's left wing political views. His bashing of President Bush on issues such as the Iraq war and the Kyoto Treaty was particularly irritating. Some readers may love his opinions, but I found them distracting at best. After about the tenth instance of his gratuitous political agenda, I finally reached the point where I wished I had not enriched Mr. Barash by buying the book.

A deceptively titled introduction to game theory
Game Theory is a subfield of mathematics and economics that simulates conflicts as games, with a payoff or loss for each decision. The major innovation is that Game Theory takes into account the importance of the other entity's decision; as in real life, conflicts aren't simply against a static opponent. This book briefly details some of the major theoretical exercises derived from game theory, such as Prisoner's Dilemma, Chicken, and others. Although this book was fairly interesting in its own right, it strangely never goes into any sort of discussion about the application of Game Theory to Biology, Ecology, or Animal Behavior, with the exception of a chapter that appears to be a last minute throw-in. It consists of a few examples where game theory has been validated in biological studies, but few are especially interesting or provoking. Those looking for any sort of mathematics (even algebra) will also be sorely disappointed, as the author decided to milk the pop-science appeal as much as possible. Although some of the discussions on the different games were interesting, the lack of even an elementary discussion of Evolutionarily Stable Strategies makes this book unlikely to appeal to those looking for what the title promises: the BIOLOGY of cooperation and competition. However, if you are disdainful of mathematics and want a fairly interesting and brief introduction to game theory, this book is probably a good place to start. The surprisingly thoughtful final chapter, on the philosophical and moral implications of game theory, carries this title slightly above mediocrity. To summarize: although this book didn't provide what I expected in terms of connecting game theory to biology, it was still an entertaining read, if not an especially enlightening one. ... Read more

Book Description

Queueing analysis is a vital tool used in the evaluation of system performance. Applications of queueing analysis cover a wide spectrum, from bank automated teller machines, to transportation and communications data networks. An introductory text, this book focuses on queueing modelling techniques and applications of data networks, examining the underlying principles of isolated queueing systems. Features include:

• Introductory chapter on pre-requisite mathematical tools
• Discussion of Markovian queueing systems, emphasising derivation techniques used to measure system performance
• Analysis of the open queueing network with a single class customer, introducing the Jackson queueing networks
• Focus on the emerging class of arrival processes, such as Markovmodulated arrival process

Book Description

In Game Theory and the Social Contract, Ken Binmore argues that game theory provides a systematic tool for investigating ethical matters. His reinterpretation of classical social contract ideas within a game-theoretic framework generates new insights into the fundamental questions of social philosophy. He clears the way for this ambitious endeavor by first focusing on foundational issues -- paying particular attention to the failings of recent attempts to import game -- theoretic ideas into social and political philosophy. Binmore shows how ideas drawn from the classic expositions of Harsanyi and Rawls produce a synthesis that is consistent with the modern theory of noncooperative games. In the process, he notes logical weaknesses in other analyses of social cooperation and coordination, such as those offered by Rousseau, Kant, Gauthier, and Nozick. He persuasively argues that much of the current literature elaborates a faulty analysis of an irrelevant game. Game Theory and the Social Contract makes game-theoretic ideas more widely accessible to those with only a limited knowledge of the field. Instructional material is woven into the narrative, which is illustrated with many simple examples, and the mathematical content has been reduced to a minimum. ... Read more

Reviews (2)

Upgrading Rawls' "Theory of Justice"
This is part one of Ken Binmore's exciting theory of the social contract taking up the discussion that took place in the 70ies after the publication of John Rawls' "Theory of Justice". While he sticks to the idea of a social contract reached through voluntary agreement in the Original Position, he also considers the utilitarian critique such as Harsanyi's. But Binmore does much more than that. He translates Rawls' metaphysical idea of a reflective equilibrium into a two-stage bargaining game with flesh and bones. He stresses the tautological character of game-theoretic tools which in this context becomes an advantage. By comparison of the ethical properties of allocations reached via competitive markets and those reached through bargaining in the original position he tries to identify a demarcation line for the decentralized aggregation of individual preferences. Binmore's book is going to be a challenge to any reader interested in the problem of explaining progress in human societies.

Classic Games like Prisoners' Dilemma applied to Social Sci
Many social scientists do not like the results and correct analysis of the game Prisoners' Dilemma and try to alter the situation by analyzing the game incorrectly. Binmore points out that what these folks want is a different model game. The problem is that these folks don't know enough game theory or utility theory. ... Read more

Book Description

"This book should appeal to readers with interests across the full spectrum from nonsmooth analysis to optimization, because it provides a clear illustration of some of the connections between these fields. The authors have done their part to nurture this important relationship..." -SIAM Review

This timely book in the area of optimization focuses on the questions of how solutions behave under perturbation, optimality conditions, and related issues. The authors have put together many results that are not easily accessible in the current literature organizing the material in a consistent manner so that a broad theory emerges. Many elements are new and not available elsewhere. ... Read more

Book Description

Introduction to the Theory of Cooperative Gamessystematically studies the main solutions of cooperative games: thecore, bargaining set, kernel, nucleolus, and the Shapley value of TUgames, and the core, the Shapley value, and the ordinal bargaining setof NTU games. To each solution a separate chapter is devoted, in whichits properties are investigated in full detail. Moreover, importantvariants are defined or even intensively analyzed. Separate chapterscover continuity, dynamics, and geometric properties of solutions ofTU games. This study culminates in uniform and coherentaxiomatizations of all the foregoing solutions (excluding thebargaining set). Except for the Shapley value such axiomatizationshave not appeared in any book. Moreover, Introduction to the Theoryof Cooperative Games contains a detailed analysis of the mainresults on cooperative games without side payments. Such analysis isvery limited or non-existent in the existing literature on gametheory. This book is of interest to Game Theorists, Economists, Mathematiciansand Researchers in Operations Research, Political Science and SocialScience. ... Read more

Book Description

This is a classic book on Queues. First published in 1961 it is clearly and concisely introduces the theory of queueing systems and is still just as relevant today. The monograph is aimed at both students and operational research workers concerned with the practical investigations of queueing, although almost every statistician will find its contents of interest. ... Read more

Book Description

This is the first systematic textbook presentation of the new microeconomic theories based on imperfect information. Each chapter explores a particular type of informational asymmetry and reviews the main contributions, from the seminal papers of the late 1960s through the most recent developments.Wherever possible the theories covered are confronted with the available experimental evidence. ... Read more

Book Description

This book is a state-of-the-art look at combinatorial games, that is, games not involving chance or hidden information. It contains a fascinating collection of articles by some of the top names in the field, such as Elwyn Berlekamp and John Conway, plus other researchers in mathematics and computer science, together with some top game players. The articles run the gamut from new theoretical approaches (infinite games, generalizations of game values, 2-player cellular automata, Alpha-Beta pruning under partial orders) to the very latest in some of the hottest games (Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex).Many of these advances reflect the interplay of the computer science and the mathematics. The book ends with an updated bibliography by A. Fraenkel and an updated and annotated list of combinatorial game theory problems by R. K. Guy. ... Read more

Book Description

Game Theory has served as a standard text for game theory courses since the publication of the First Edition in 1968. The Third Edition updates several recently developed subfields. It adds fresh chapters on subjects such as games with incomplete information and spatial games. Owen has expanded "Two-Person General-Sum Games" into two chapters, the second becoming "Two-Person Cooperative Games." There are new sections in the chapters "Two-Person Cooperative Games" and "Indices of Power," and there is new information throughout the book on non-cooperative games. Game Theory remains the only book to cover all salient aspects of this field that, having displaced Keynesian economics, is making inroads throughout the social sciences.

Key Features
* Explains work of 1994 Nobel Prize Winners
* Full expansion of cooperative game theory sections
* Covers games with incomplete information
* Spatial games section features many illustrations
* Updated bibliography ... Read more

Reviews (1)

Well written, unfortunately it contains many misprints
I believe this book to be an excellent introduction to game theory, also for self - study purposes. Unfortunately, it seems to contain too many misprints, which are particularly annoying if it is used for self study: You always wonder,whether you are wrong, or the book is. This is all the more amazing as I read the third edition. ... Read more

Book Description

A thorough and highly accessible resource for analysts in a broad range of social sciences.

Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods.

Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root-finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include:

• More than 200 geometric interpretations of algebraic results, emphasizing the intuitive appeal of mathematics
• Classic results mixed with modern numerical methods to aid users of computer programs
• Extensive appendices containing mathematical details important for a thorough understanding of the topic

With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science,geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences. ... Read more

Reviews (1)

Good Reference for Optimization
This book carefully describs the fundamental and application of optimization. You can easily find the useful approach when you try to optimize your problem and know how to use it with the help of step-by-step illustration of that approach. ... Read more

Book Description

Game theory, defined in the broadest sense, is a collection of mathematical models designed for the analysis of strategic aspects of situations of conflict and cooperation in a broad spectrum of fields including economics, politics, biology, engineering, and operations research. This book, besides covering the classical results of game theory, places special emphasis on methods of determining `solutions' of various game models. Generalizations reaching beyond the `convexity paradigm' and leading to nonconvex optimization problems are enhanced and discussed in more detail than in standard texts on this subject. The development is theoretical--mathematical interspersed with elucidating interpretations and examples.Audience: The material in the book is accessible to PhD and graduate students and will also be of interest to researchers. Solid knowledge of standard undergraduate mathematics is required to read the book. ... Read more

Book Description

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references. ... Read more