Book Description

One of the definitive works in game theory, this volume takes an original and expert look at conflict solutions. Drawing on game theory, the calculus of variations, and control theory, the author solves an amazing array of problems relating to military situations, pursuit and evasion tactics, games of firing and maneuver, athletic contests, and many more. Clearly detailed examples; numerous formal calculations. 1965 ed.
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Reviews (1)

Differential Games
This is the original book on differential games. It is as relevant today as when it was written nearly 40 years ago. The book introduces all the main concepts and equations in differential games. This is achieved without recourse to heavy theorems or proofs. A central feature is the use of many and varied examples of differential games; the homoicidal chauffeur, wars of attrition, pursuit with a rocket, etc. These bring the whole field alive with potential. Another element is the use of geometry and pictures to describe game evolution. This book is a must for anyone interested in modern autonomous systems. ... Read more

Book Description

A modern, up-to-date introduction to optimization theory and methods
This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization.
Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides:
* A review of the required mathematical background material
* A mathematical discussion at a level accessible to MBA and business students
* A treatment of both linear and nonlinear programming
* An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods
* A chapter on the use of descent algorithms for the training of feedforward neural networks
* Exercise problems after every chapter, many new to this edition
* MATLAB(r) exercises and examples
* Accompanying Instructor's Solutions Manual available on request
An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business. ... Read more

Reviews (3)

Not For Undergraduates
This book should not be used to teach an Introduction to Optimization at the undergraduate level. It is being done so at my school, and it is driving the undergraduate students crazy because they do not understand the book, the notation also is causing problems. If you are new to the subject area, and do not have an advanced math background(more than college) try looking elsewhere.

took the class, liked the book
Drs. Chong and Zak are Professors of Electrical Engineering at Purdue, and Dr. Chong was the instructor for the ECE grad level optimization class when I took it spring '97. The book alone is good, detailed and rigorous enough for a graduate course without sacrificing readability or in-chapter examples. However, without the MATLAB examples that were developed by the authors to accompany lectures and illustrate each optimization method covered, the material might be a little abstract or dry for self-teaching. An excellent introduction or reference nonetheless, those without a solid base in linear algebra should keep a reference text handy while reading.

All industrial engineering student should buy this book.
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Book Description

"Game theory in its glory. This collection is a parade of deep insights and beautiful ideas led by of one of the most influential economic theoreticians of his generation." -- Ariel Rubinstein, Professor of Economics, Tel-Aviv University and Princeton University

Robert Aumann's groundbreaking career in game theory has spanned over 35 years. These two volumes provide convenient access to all of his major research--from his doctoral dissertation in 1956 to papers as recent as January 1995. Threaded through all of Aumann's work (symbolized in his thesis on knots) is the study of relationships between different ideas, between different phenomena, and between ideas and phenomena. "When you look closely at one scientific idea," writes Aumann, "you find it hitched to all others. It is these hitches that I have tried to study."

The papers are organized in several categories: general, knot theory, decision theory (utility and subjective probability), strategic games, coalitional games, and mathematical methods. Aumann has written an introduction to each of these groups that briefly describes the content and background of each paper, including the motivation and the research process, and relates it to other work in the collection and to work by others. There is also a citation index that allows readers to trace the considerable body of literature which cites Aumann's own work. ... Read more

Book Description

One of the problems in economics to which economists have devoted a considerable amount of attention in recent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it must be asked under what circumstances such an equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems. These outline the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for cooperative and non-cooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. In addition, the author presents new proofs of old results in order to further clarify the results. He also proposes new results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students. ... Read more

Reviews (2)

An excellent survey of more than fixed point theorems.
The author compiles theorems, definitions, and properties on a number of topics. There's some convex analysis, maximization of binary relations, fixed point and selection theorems, and various sufficient conditions for existence of equilibria in games and economies.

A nice feature is that the author explains the equivalence or interconnectedness of theorems from different classes -- comparing the KMM lemma to Brouwer's fixed pt. thm., for instance.

This book is extremely useful for its many variations on common principles. Researchers can benefit from consulting it when they have a problem which does not satisfy the usual criteria -- for instance, if you ever have to ask, "I have a correspondence which satisfies all the conditions for Kakutani's theorem except that it is l.h.c. rather than u.h.c.; am I still able to guarantee a fixed point?"

Grad students in micro/game theory can benefit from the survey of theorems, and familiarizing themselves with the many ways they can get to desired results.

The book is compact and thorough with little exposition. Definitions are very clear, and the author is very good at noting when definitions vary, or the same term has multiple definitions in the literature. Though it presents itself as a mathematical text, its audience is clearly economists -- the conditions given and situations described are clearly ones that economists will recognize, and the applications are economic.

A very nice book for people who already know the applications of such theorems and who need minimal explanation.

the best buy
The author, one of the most prominet professors in mathematical economics surveyed fixed point theorems. The theorems are often used to prove the existence of solutions in game theory and economics. If you major in mathematical economics or game theory, you can't avoid to buy this book. ... Read more

Book Description

N-person game theory analyzes contests in which there are more than two sets of conflicting interests, e.g. a hand of poker or wide-scale warfare. In this sequel to his Two-Person Game Theory, the author introduces the necessary mathematical notation (mainly set theory), presents basic concepts, discusses a variety of models, and provides applications to social situations.
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Book Description

Here's something to do at your next dinner party after the guests have wined and dined, tell them you're auctioning off a dollar--a plain U.S. one-dollar bill. But set the rules as follows: while the winner gets the dollar, the second-highest bidder must also pay the amount of his last bid, even though he gets nothing.

If you can get a single one-cent bid, chances are the auction will go to fifty cents. If someone bids fifty-one cents, bidding will almost certainly reach a dollar. If it goes to one dollar and one cent, the sky's the limit. No one wants to be the second-highest bidder. Afterwards the bidders say they spent so much because their opponent "went crazy," which is a little like saying "the fight started when he hit me back."

Everyone has gotten into situations that resembled the dollar auction--where they devoted way too much effort to something not worth the commitment, because the cost of giving up was worse.

Why do we act this way? How can we recognize these traps before we're in too deep? Is there such a thing as rational behavior, and if so, how do we use it to our advantage?

Hungarian mathematician Laszlo Mero introduces us to the basics of John von Neumann's game theory and shows how it illuminates such aspects of human psychology as altruism, competition, and politics. Mero covers such concepts as zero-sum games; Prisoner's Dilemma; the game of Chicken (played with cars in Rebel Without A Cause), where logic proves that the rational strategy is to be irrational; how to be kind to your lover through game theory; and when the Golden Rule works and when it leads to disaster.

Mero shows how game theory is applicable to fields ranging from physics to evolutionary biology, and explores the role of rational thinking in the context of real-life situations ranging from doorway etiquette to the nuclear arms race. He also explains how moral dilemmas arise; how to act rationally and ethically when they do; and how the intersection of rationality and irrationality inevitably becomes what we call "wisdom." This fascinating, urbane book shows us how we can better understand ethical behavior. ... Read more

Reviews (6)

Interesting book
The book is divided into three parts:

I. Introduces some concepts from game theory, psychology
II. Gives examples from fields of economics, physics, biology
III. Discusses rationality and irrationality.

I found the first two parts both helpful and easy to read. They weren't technical at all, there isn't a single formula in the book. However, the last part is very hard to read and understand. I had to re-read some sentences several times and am not sure if I followed the author correctly.

Overall, I would suggest reading the book - it won't take much time and you can learn such concepts as evolutionary stable strategies, mixed strategies. Also, presentation of some concepts from physics and economics is interesting.

Great for learning about Game Theory
This book is fascinating in how it demonstrates what we do in politics, science, and even meditation can affect our rational (and irrational) decision making processes, both individualy and in community.

I actually got referred to this book by a website that discussed Game Theory and when I went to Amazon to purchase it, I was amused by the reviewers on Amazon that were horrified that the last of the book covered Meditation/Mysticism. Thats what absolutely convinced me to buy it. I am a scientist and I am practicing meditation, I see both sides.

Mero does a great job of showing how Game Theory can explain the Rational and also show how irrational we are. He practically predicts why the reviewers that didn't like the last parts of his book are the way they are, which of course made them say the things they say in the review!

As the famous ad says, Just do it.

For crying out loud, NEVER play the dollar auction!
In this book, Mero adds some flesh to game theory, explaining why so many people become entranced with how it sets up economic and social choices as toy puzzles, in which people are trying to get the best possible outcome.

In particular, he explains some of the more infamous non-zero-sum games: the dollar auction, in which a dollar bill is auctioned off, but with a twist - both the highest bidder and the second-highest bidder must pay their bids, but only the highest bidder gets the dollar; and the prisoner's dilemma (and its variants), in which cooperation is the best result for the 2 players combined, but there's the danger of being undermined by the other player and individually losing everything. The dollar auction is likened to an arms race (indeed, the U.S. won =that= particular dollar auction against the Soviets), where what is being bought is military supremacy between superpowers. The prisoner's dilemma can be likened to a situation like a lane closure on a busy highway: if one merges in turn, and everybody else does, traffic keeps flowing somewhat; however, if only one person zooms ahead and merges ahead of where they should in fairness, the traffic can still go on fine and that one zoomer gets a benefit over the other drivers. But if =everybody= tries to cut in line... traffic clog.

It is true that trying to extend game theory to morality is a tricky business, and as another reviewer has put it, the book gets downright embarrassing towards the end. However, I am a math teacher, and have used ideas from the book to put more =oomph= in my classes on game theory to gifted teenagers. There isn't much in the way of math in here, but plenty of rational thinking and can lead a little light on to why game theory research has led to the winning of a Nobel Prize in Economics (or two).

An interesting book gets very, very strange.
Mero's book is an interesting read, and is a very good non-mathematical review of the basics of game theory and its relationship to human ethics. I suspect that its translation from Hungarian led to its sometimes strange choices of words, but on the whole, it is a good way to get a sense of the surprising generality and importance of the subject.

Unfortunately, the book is marred by Mero's expansion of game theory into a "theory of everything". By the last chapter, he has gone from straightforward applied mathematics into fuzzy-headed mysticism. At this point, the book has become more embarassing than interesting. My suggestion is to read the first half of tbe book and forget the rest!

A very well written and important book
I found this book compelling: an understandable, non-dogmatic, open-minded, non-technical yet scientific look at how mathematical game theory might be applied by someone trying to behave morally in a universe of limited resources. The concepts are clearly stated without jargon in such a way that people with little aptitude or patience for mathematics will remain interested throughout. An important book for anyone interested in morality at any level. ... Read more

Book Description

Nine catchy songs teaching students addition facts with sums up to 18. A complement of self quizzing tracks allows students to quiz themselves.

Ages: 6 - 7 ... Read more

Reviews (1)

My 7 year old loves it!
My daughter and I were more than pleased with this math CD. I'm pleased with the music style -catchy tune AND understandable, no rap. I also like the fact that each addition is repeated. Although my daughter knows how to add she still uses her fingers sometimes, I have found that this has helped her to memorize facts more easily. The singing book that comes along is a big plus! I would also recommend the Multiplication unplugged because it teaches how to count by 2s,3s,etc. ... Read more

Book Description

This book is a comprehensive, self-contained survey of the theory and applications of differential games. No prior knowledge of game theory is assumed, although a basic knowledge of linear algebra, ordinary differential equations and mathematical programming is required. This book is designed as a research resource for researchers and scholars as well as a text for advanced undergraduates and first year graduate students. Those in all aspects of economics, as well as in industrial organizations, decision sciences, management science, marketing, operations research and quantitative methods will benefit from this book. ... Read more

Book Description

Catchy melodies, drill and student involvement make division facts with divisors to 9 very memorable. ... Read more

Reviews (2)

A Wonderful Resource
I recently purchased and tried Division Unplugged as a remedial resource for my grade five students. I found it to be thoughtfully constructed and that the songs were quite musically done. Each song not only teaches division facts, but reviews them by reminding the student of the multiplication tables. The choruses of each of the songs also incorporate skip counting, so even the slowest of students is able to make the connection between multiplication facts and division questions. Great job. I would recommend it to anyone.

Division Unplugged
I was a little disappointed with the content of division unplugged. Learning how to count by 2's and 5's is all that I learned from listening to the CD. Each song sounded exactly the same. There was a plus to this purchase though, the brain teasers at the end of the booklet were helpful. ... Read more

Book Description

Developments in optimization theory, including emphasis on large problems and on interior-point methods for linear programming, have begun to appear in production software.Here is a reference tool that includes discussions of these areas and names software packages that incorporate the results of theoretical research.After an introduction to the major problem areas in optimization and an outline of the algorithms used to solve them, a data sheet is presented for each of the 75 software packages and libraries in the authors' survey.These include information on the capabilities of the packages, how to obtain them, and addresses for further information.

Standard optimization paradigms are addressed -- linear, quadratic, and nonlinear programming; network optimization; unconstrained and bound-constrained optimization; least-squares problems; nonlinear equations; and integer programming.The most practical algorithms for the major fields of numerical optimization are outlined, and the software packages in which they are implemented are described.

This format will aid current and potential users of optimization software in classifying the optimization problem to be solved, determining appropriate algorithms, and obtaining the software that implements those algorithms.Readers need only a basic knowledge of vector calculus and linear algebra to understand this book. ... Read more

Book Description

Many of us remember playing the game Dots-and-Boxes as children. It is a familiar paper-and-pencil game for two players who start from a square or rectangular array of dots and take turns in joining two horizontally or vertically adjacent dots. If a player completes the fourth side of a square (box), he initials that box and must then draw another line. When all the boxes have been completed, the game ends and whoever has initialed more boxes is declared the winner. Dots-and-Boxes is, like other good games, remarkable in that it can be played on several different levels of sophistication.This deceptively simple game, however, is more than just child's play.Dots-and-Boxes strategy serves as an introduction to mathematical game theory, a subject that has earned the prominent mathematician John Nash a Nobel Prize in Economics. This book is an essential guide to the game of Dots-and-Boxes and its mathematical underpinnings. Chapters on strategy are interspersed with 100 sample problems and their strategic solutions.The book will appeal to a diverse range of readers, from casual players seeking to improve their play to mathematicians interested in the more sophisticated strategy techniques. ... Read more

Reviews (3)

The only book about Dots and Boxes to my knoweledge
This book is one of a kind, and will show you that the game of Dots and Boxes is far from trivial, in spite of the common idea. It will also show you some very high-quality technical stuff about this game.The main issue is that the book is born as a collection of problems, and the try to turn it into a full-fledged book wasn't completely successful. The explanations are lacking in clarity and the result is that you have a very good series of positions and problems, but not the knoweledges for solving them

Incomplete
Although the subject matter is enticing and the introduction thorough, the text proper falls short. The examples come with minimal, if any, explanation, leaving it to the reader to actually make conjectures and prove lemmas. This book seems to have been writtem more as a private notebook for someone who already understands the game rather than an explanation for neophytes.

Detailed analysis of a simple game
The title game of this book is the simple one where two players start with a rectangular grid of dots. They take turns connecting two adjacent dots using either a horizontal or vertical line. If the line closes a square, the player initials it and then connects two additional dots. The player with the most initialed squares at the end wins the game. There are several games that are mathematically equivalent, which makes the explanations even more interesting.
Like so many other games, the rules are simple, effective strategies for improved play are available and easy to understand, but a complete analysis is elusive and may be all but combinatorially impossible. Of course, this is what keeps our interest.
Many problems with solutions are presented with some currently unsolved situations listed at the end. While the book is interesting, the lack of detailed explanations of at least some of the solutions would have done a great deal to improve the quality of the book. Games like this have strategies that can be subtle to say the least and I found it difficult to justify the moves that the author put forward as the appropriate strategy. However, this is not to say that I ultimately found the move to be incorrect.
Humans are creatures that require games and play. The best all seem to be the ones with simple rules and complex or impossible strategies. The games described in this book are fun to play and the explanations of basic strategies are easy to understand. If this type of game interests you, then you will find the book enjoyable.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

Book Description

Numerical Optimization has numerous applications in engineering sciences, operations research, economics, finance, etc. Starting with illustrations of this ubiquitous character, this book is essentially devoted to numerical algorithms for optimization, which are exposed in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. The theoretical bases of the subject, such as optimality conditions, Lagrange multipliers or duality, although recalled, are assumed known. Most of the algorithms described in the book are explained in a detailed manner, allowing straightforward implementation. This level of detail is intended to familiarize the reader with some of the crucial questions of numerical optimization: how algorithms operate, why they converge, difficulties that may be encountered and their possible remedies. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions. ... Read more

Book Description

Important text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols.
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Book Description

Book Description

Book Description

Evolutionary game theory attempts to predict individual behavior (whether of humans or other species) when interactions between individuals are modeled as a noncooperative game. Most dynamic analyses of evolutionary games are based on their normal forms, despite the fact that many interesting games are specified more naturally through their extensive forms. Because every extensive form game has a normal form representation, some theorists hold that the best way to analyze an extensive form game is simply to ignore the extensive form structure and study the game in its normal form representation. This book rejects that suggestion, arguing that a game's normal form representation often omits essential information from the perspective of dynamic evolutionary game theory.

The book offers a synthesis of current knowledge about extensive form games from an evolutionary perspective, emphasizing connections between the extensive form representation and dynamic models that traditionally have been applied to biological and economic phenomena. It develops a general theory to analyze dynamically arbitrary extensive form games and applies this theory to a range of examples. It lays the foundation for the analysis of specific extensive form models of behavior and for the further theoretical study of extensive form evolutionary games. ... Read more

Book Description

Noted expert’s clearly written discussions of essential ideas of highly useful mathematical approach to human behavior and decision-making. Lucid, accessible treatment of such concepts as "utility," "strategy," and the difference between "non-zero" and "zero-sum" games. Minimum of mathematical prerequisites makes it accessible to non-mathematicians.
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