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1. Handbook of Applied Optimization
$87.75 $50.00 list($93.75)
2. Games of Strategy
$88.96 $73.54 list($99.95)
3. The Statistical Analysis of Failure
4. Game Theory: Analysis of Conflict
$118.30 $63.76 list($130.00)
5. Multi-Objective Optimization Using
$32.97 $31.90 list($49.95)
6. 3D Math Primer for Graphics and
$110.00 $49.89
7. Fundamentals of Queueing Theory
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8. The Compleat Strategyst: Being
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9. Game Theory: A Nontechnical Introduction
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10. Queueing Networks: Customers,
11. The Mathematics of Games and Gambling
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12. The Essential John Nash
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13. Numerical Optimization
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14. On Numbers and Games
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15. Game Theory and the Social Contract,
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16. Dynamic Optimization
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17. A First Course in Optimization
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18. Winning Ways for Your Mathematical
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19. The Theory of Learning in Games
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20. Winning Ways for Your Mathematical

1. Handbook of Applied Optimization
by P. M. Pardalos, Mauricio G. C. Resende, Panos M. Pardalos
list price: $225.00
our price: $225.00
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Asin: 0195125940
Catlog: Book (2002-04-01)
Publisher: Oxford University Press
Sales Rank: 172234
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2. Games of Strategy
by Avinash K. Dixit, Susan Skeath
list price: $93.75
our price: $87.75
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Asin: 0393974219
Catlog: Book (1999-06-01)
Publisher: W.W. Norton & Company
Sales Rank: 217713
Average Customer Review: 4 out of 5 stars
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Book Description

All introductory textbooks begin by attempting to convince the student readers that the subject is of great importance in the world, and therefore merits their attention. The physical sciences and engineering claim to be the basis of modern technology and therefore of modern life; the social sciences discuss big issues of governance, for example, democracy and taxation; the humanities claim that they revive your soul after it has been deadened by exposure to the physical and social sciences and to engineering. Where does the subject "games of strategy," often also called game theory, fit into this picture, and why should you study it? Dixit and Skeath's Games of Strategy offers a practical motivation much more individual and closer to your personal concerns than most other subjects. You play games of strategy all the time: with your parents, siblings, friends, enemies, even with your professors. You have probably acquired a lot of instinctive expertise, and we hope you will recognize in what follows some of the lessons you have already learned. This book's authors will build on this experience, systematize it, and develop it to the point where you will be able to improve your strategic skills and use them more methodically. Opportunities for such uses will appear throughout the rest of your life; you will go on playing such games with your employers, employees, spouses, children, and even strangers. Not that the subject lacks wider importance. Similar games are played in business, politics, diplomacy, wars--in fact, whenever people interact to strike mutually agreeable deals or to resolve conflicts. Being able to recognize such games will enrich your understanding of the world around you, and will make you a better participant in all its affairs. ... Read more

Reviews (6)

5-0 out of 5 stars Excellent Starter
I'm learning game theory on my own and found this book an excellent starter. The book provides a wide range of topics, building from what strategy means in game theory, to the sequential and simultanous play of games, to more specialized areas and applications of the theory.

Although it keeps the mathematics rather minimal, you'll need to do your own workings to better understand the text. To get more from this book, you'll need to be involved in the examples the book provides... breezing through may not help you understand the theory better.

While I do read other books on game theory, I find myself going back to Games of Strategy to review the basics and the examples. The example on the tennis game has provided me some starting ideas on the issues I've to face in some research areas I'm working on.

3-0 out of 5 stars From a student perspective
I used this book as a student in an undergraduate Game Theory course and have mixed feelings about it.

Positives: the book is written in a simple style with relatively good examples that promote conceptual understanding.

Negatives: the book is very poorly laid out. Some chapters don't seem to follow any logical progression, so the reader must frequently jump from one section to another. Additionally, the book doesn't utilize some fairly standard terms, and the index doesn't facilitate the book's use as a reference manual.

The reason I wrote this review was because I came online to try to find a better Game Theory textbook -- I ran into problem studying from this one.

4-0 out of 5 stars Good and interesting introduction to game theory
I really enjoyed this book. There were some areas where it was kind of confusing, but I found that overall it kept me interested. Their approach is good especially for those who want to learn about the topic and its applications but don't have much background in math or economics. Game theory is a really interesting field, and this text provides a good introduction for those who want to learn about it without getting bogged down in the math. The book does its best job I think in tying the principles to the real world.

5-0 out of 5 stars Excellent Textbook
I used this book when teaching an undergraduate course in game theory at Smith College. The course had a one semester calculus prerequisite and no econ prerequisites. The book is fantastic. It makes material very accessiable to students. It provides very interesting examples.

3-0 out of 5 stars Why won't anyone just call it the Battle of the Sexes?
I used this book for the second half of a principles of micro. course, to supplement the shoddy, one-chapter-on-the-Prisoners'-Dilemma treatment found in most principles textbooks. Everything said here should be interepreted according to this. From this instructor, the book gets points for being the best one available for teaching low-level undergraduates, but it could have been a LOT better. For example:

The notation and terminology are in many cases non-standard, and tend to change from chapter to chapter. The BoS is the Battle of Cultures (though this is not the first book to mess with this game). Chicken is a Game of Assurances, except in Ch. 10. SPE are (quasi-)formally described in Ch. 6, but they are actually introduced in Ch.4, where they are called Rollback Equilibria. Many times, I would have to tell students, "this is what your book calls a..."

The authors use confusing and convoluted examples to motivate concepts. For example, it takes a confusing, two-page story about advertizing in a political race to motivate study of sequential-move games. A simple entry-deterrence story gets the point across.

Also on this point, sequential-move games appear before simultaneous-move ones. I reversed this, in part ot be able to show that the set of SPE is merely a subset of the set of NE (again, using the entry-deterrence story). In fact, there's no real attempt to relate many of (seemingly unrelated) concepts to one another, as equilibrium refinements, each of which conforms to some intuitive concept of the "right" way of playing a given game.

The disucssion of the special case of two-person, zero-sum games, introducing pre-Nash notation and solution concepts is merely confusing for the uninitiated. I see no reason that anyone not yet in graduate school should have to know the min-max theorem.

In some ways, the books seems to suffer from over- and under-reach at the same time. The subject of infinitely repeated games gets two pages on TFT and Grim strategies in a repeated Prisoners' Dilema. There's no real discussion of rationalizability, or Bayesian games; many important concepts are smooshed into a couple of chapters, like they're being swept under the rug. There IS, however, a chapter on evolutionary games, and a (math-free) chapter on auctions.

Again, these are points that, I think, led to undue confusion, and required undue effort to counteract. However, I don't mean to be unduly harsh. I'm not suggesting that the authors should merely have mimeographed Fudenberg & Tirole, and whited-out the math. This is a useful book, ahead (as far as I know) of other treatments appropriate for students at this level. But it could have been much better. ... Read more

3. The Statistical Analysis of Failure Time Data (Wiley Series in Probability and Statistics)
by John D.Kalbfleisch, Ross L.Prentice
list price: $99.95
our price: $88.96
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Asin: 047136357X
Catlog: Book (2002-08-23)
Publisher: Wiley-Interscience
Sales Rank: 418639
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Book Description

* Contains additional discussion and examples on left truncation as well as material on more general censoring and truncation patterns.
* Introduces the martingale and counting process formulation swil lbe in a new chapter.
* Develops multivariate failure time data in a separate chapter and extends the material on Markov and semi Markov formulations.
* Presents new examples and applications of data analysis.
... Read more

4. Game Theory: Analysis of Conflict
by Roger B. Myerson
list price: $29.95
our price: $29.95
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Asin: 0674341163
Catlog: Book (1997-09-01)
Publisher: Harvard University Press
Sales Rank: 28061
Average Customer Review: 4.83 out of 5 stars
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Reviews (6)

5-0 out of 5 stars Masterpiece
This book is a masterpiece: it goes from the simple and straightforward (with examples of sequential equilibria) to technical and challenging material (such as the Mertens-Zamir type space). I own Fudenberg-Tirole and Osborne-Rubinstein, but it is Myerson that gets picked up the most. What I find most rewarding is that Myerson introduces everything gently, working from examples to build a general theory.

4-0 out of 5 stars not bad
very comprehensive book. Covers pretty much everything. It's supposed to be a graduate text but undergrads can handle it as long as they know some math and aren't too scared by all the notation. Oh and Myerson is nice guy too.

5-0 out of 5 stars still on the frontier because of disinformation
This book is not good only because it explains all well known difficult concepts which noone so far has been able to explain clearly and rigourosly in one book but for new important topics that are less known for the majority of game theorists. I'm refering to the idea of networks and cooperation structures and also cooperation under uncertainty with the idea of virtual utility.

5-0 out of 5 stars The Best Book for Learning Pure Game Theory
Myerson's book is fantastic. For learning the *theory* of game theory, it is the best book available. Virtually every important topic in game theory is treated at some point in the book (though students are not always beaten over the head with their names).

The plan is well thought out and has some interesting innovations. For example, incomplete information is well integrated and permeates the text in many places, rather than one or a couple chapters. However, beacuse of this -- while the book is superb for learning and developing understanding -- it is not always the best reference. Some topics are not available in one easily indexed locations. (On the other hand, other topics like bargaining and zero sum games are treated in the usual discrete way.)

5-0 out of 5 stars An Elegant and Deep Treatment
I just completed a game theory book (Game Theory Evolving, Princeton University Press, 2000). To find the best way to present various materials, I went through virtually every game theory book in existence. For the presentation of the basic material on normal and extensive form games, nothing even came close to this book in clarity of presentation and depth of understanding of the issues. Most textbooks, even highly touted ones that are mathematically challenging, do not even come close, and rarely even present the material in a coherent form at all.

I used to do a lot of carpentry, and I always knew the good carpenters from the run of the mill. The latter talk about how to build stuff. The good ones talked about how you choose, preserve, treat, and sharpen your tools. Myerson is, for game theory, like the good carpenter, and this book is more about the nature of the tools of game theory than their deployment--although it is certainly that, too.

The subtitle of this book is silly ("The Analysis of Conflict"). Game theory is the analysis of cooperation as much as conflict, and much, much else as well. So is this book. ... Read more

5. Multi-Objective Optimization Using Evolutionary Algorithms
by Kalyanmoy Deb, Deb Kalyanmoy
list price: $130.00
our price: $118.30
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Asin: 047187339X
Catlog: Book (2001-06-27)
Publisher: John Wiley & Sons
Sales Rank: 427739
Average Customer Review: 4.5 out of 5 stars
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Book Description

Evolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run.
· Comprehensive coverage of this growing area of research
· Carefully introduces each algorithm with examples and in-depth discussion
· Includes many applications to real-world problems, including engineering design and scheduling
· Includes discussion of advanced topics and future research
· Can be used as a course text or for self-study
· Accessible to those with limited knowledge of classical multi-objective optimization and evolutionary algorithms
The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.
... Read more

Reviews (2)

4-0 out of 5 stars Great book; a must for engineers and scientists alike
Kalyanmoy Deb has put together a great summary of the state of affairs in multiobjective genetic algorithms. Should you be an engineer or a scientist involved in the optimization of any design of sizeable complexity, you should read this book and become familiar with the techniques that have evolved over the last decade into powerful methods of optimization. This book is in many many ways bridging the gap from Michalewicz's and Fogel's book ("How to solve it") to the more modern era of this field (eg late nineties up to now...). So whereas those two authors never really considered multiobjective genetic algorithms, Deb plows through with the great expertize of a (perhaps even "the") leading researcher in that domain. This is a great book of _receipes_ with the level of details necessary to make use of them. It's a "how to" book; this is the one you have cracked open on your desk while you're hard coding it all up. However, it's not very well written with the prose being very terse and basically quite unengaging. But so what! In some sense yes perhaps, but Michalewicz and Fogel made a point that one can write technical litterature that one can also read. Perhaps they went overboard... in any case, Deb's book is about algorithms so who cares about whether the book puts you to sleep and it can do that, unfortunately. Apart from the unengaging style and the paucity of depth in the examples scope, the real problem with the book is not with the book itself, it's with the field of multiobjective optimization based on evolutionary methods. It's fairly evident that there is not much of any sort of fundamental understanding available at this time in support of why evolutionary techniques do work well, and they do, sometimes... If this understanding is available, you won't find it in Deb's book. If you are like me though, you won't care all that much really so long as the techniques are efficient and presented in a way that make them useable, and that's done right... But on the whole, it's a little unsatisfying because one's left with a panoply of various techniques and ways to define operators and representations but there is no insight given on which one might be best or how to craft them to particular situations. There is a lot of so-'n-so in reference this and that did it like this and it seems to work well there, however... The reason for this state of affairs is, of course, that nobody has a real clue, yet... But that is _not_ Deb's fault and this is not why, as a user, I'm not rating his book a full 5 stars. In some sense it could be rated as high as that but I thought the presentation was rather unengaging and not with all the breath and depth it could have had. So it's a 4.5 stars perhaps... let's say... but Amazon does not let me select 4.5 stars so it's 4, this edition at least...

5-0 out of 5 stars The Reference in Evolutionary Multiobjective Optimization
This is the first complete and updated text on Multi-objective Evolutionary Algorithms (MOEAs), covering all major areas clearly, thoughtfully and thoroughly. Thanks to the development of evolutionary computation MOEAs are now a well established technique for multi-objective optimization that finds multiple effective solutions in a single run. The widely interdisciplinary interest of engineers, scientists and mathematicians towards MOEAs has been evident during the first international conference on this topic (EMO2001,Zurich). The book is extremely useful for researchers working on multi-objective optimization in all branches of engineering and sciences, that will find a complete description of all available methodologies, starting from a detailed description and criticism of classical methods, towards a deep treating of the most advanced evolutionary techniques. Moreover several analytical test cases are given, covering all difficulties a MOEA encounters when converging towards the Pareto Optimal front. This set of test problems, together with several performance measurement parameters are essential when testing a new strategy before its application to a real-world problem. Despite the detail in advanced topics, Deb's book may be also used as a reference-book for a post-graduate course thanks to the scholarly coverage of basic arguments. As a final remark I strongly suggest everyone working on evolutionary computation and optimization to keep this book on the desk. ... Read more

6. 3D Math Primer for Graphics and Game Development
by Fletcher Dunn, Ian Parberry
list price: $49.95
our price: $32.97
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Asin: 1556229119
Catlog: Book (2002-06-15)
Publisher: Wordware Publishing
Sales Rank: 12069
Average Customer Review: 4.44 out of 5 stars
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Book Description

3D Math Primer for Graphics and Game Development covers fundamental 3D math concepts that are especially useful for computer game developers and programmers. The authors discuss the mathematical theory in detail and then provide the geometric interpretation necessary to make 3D math intuitive. Working C++ classes illustrate how to put the techniques into practice, and exercises at the end of each chapter help reinforce the concepts.

This book:

* Explains basic concepts such as vectors, coordinate spaces, matrices, transformations, Euler angles, homogenous coordinates, geometric primitives, intersection tests, and triangle meshes.

* Discusses orientation in 3D, including thorough coverage of quaternions and a comparison of the advantages and disadvantages of different representation techniques.

* Describes working C++ classes for mathematical and geometric entities and several different matrix classes, each tailored to specific geometric tasks.

* Includes complete derivations for all the primitive transformation matrices. ... Read more

Reviews (18)

5-0 out of 5 stars Very good book to get started with
The authors state early on that this book is intended as the first book an aspiring game programmer should read, and I would agree that for the most part it lives up to that goal. Many 3D game programming books include math primers covering a chapter or two, but really, 3D math is a huge topic deserving an entire volume. This book provides a great service, then, in that it thoroughly covers most of the basic topics that graphics programmers need to know, in a tutorial style that should be accessible to all beginners. Hopefully, we'll start to see more game programming books that focus on their core material and defer coverage of 3D math to books like this one rather than trying to pack unavoidably incomplete coverage into a few dozen pages.

So, what exactly does it cover? It starts off with a couple of chapters on coordinate systems, and then spends three chapters on vectors, followed by another three chapters on matrices and transformations. It then covers orientation, comparing matrix, Euler angle, and quaternion representations (including one of most clear explanations of quaternions that I've encountered), before diving into several chapters covering geometric primitives, including detailed coverage of working with triangle meshes.

The book closes with a chapter applying 3D math to graphics in areas such as lighting, fog, coordinates spaces, LOD, culling and clipping, and so on, and another chapter on visibility determination, touching on things like quad- and octrees, BSP trees, PVS, and portal techniques. The explanations in these chapters are much less complete, taking more of an overview approach. Others have criticized the book for this, but I feel that an overview is appropriate, since it then sets the stage for these topics to be covered in detail in other game programming books.

I'd definitely recommend this book to anyone just getting started with game and graphics programming.

5-0 out of 5 stars Best bet for getting a solid understanding of 3D math
Our goal in writing this book was not to cover as many topics as possible, like some other books, but rather to hit the most important concepts thoroughly. If you are a beginner, or have some "holes" in your understanding of matrices, Euler angles, left-handed vs. right-handed coordinate spaces, or key graphics concepts like zoom or the lighting equation, this book is for you.

A feature of this book over other books is the extent to which we have tried to develop the reader's geometric intuition, rather than just presenting numbers and equations. We show what the geometric interpretation of each mathematical operation is, why you would ever use that operation, and, in many cases, how the equation was derived in the first place. We do not gloss over "minor details" such as row vectors versus column vectors, or left- versus right-handed coordinate spaces. These "minor details" make all the difference in the world when you are trying to use an equation out of a book.

For the more advanced reader, we offer some of the clearest and complete discussions of some more advanced topics such as quaternions and barycentric coordinates. The book can be used as a reference for many important vector and matrix operations and identities. It also has a toolkit of many important equations for geometric primitives and intersection tests.

Our focus is on theory, so the book is not a big code dump like many books. The code we have provided consists primarily of "utility" classes for vectors, quaternions, and matrices. I think you will find that our code is simpler to read and understand than most code you will find elsewhere. We also offer some unique and thoughtful advice on good class design, specifically targetted to classes for doing 3D math and getting it right the first time, without twiddling minus signs or swapping numbers experimentally until it looks right



5-0 out of 5 stars the best book on math now
this book assume your beginner in that filed .
authors covers alot of topics in math and its application in a clear style with pictures,examples and finally code !.
i recommend this book for beginners in game programming .

Ahmed Saleh , Computer Graphics Programmer .

5-0 out of 5 stars Deceptively good book
I need to create a 3d math library for a project I was working on and wanted to take a look at some book on the subject. This one looked like one of the 14 year old 'how to make a video game' type books and I wasn't expecting much, however I was pleasantly suprised by the depth of the 3d mathematics in the book.
As an example i was unclear about how to calculate the inverse matrix correctly for an n-dimension matrix and the book goes over calculating adjucts and determinats, and inverses for a n-dimensional matrix both supplying the general math and some C code. The code i didn't find helpful, simply because I coding in the python c api and not straight c, however it could be helpful to someone writing in C.
I would recommend this book to anyone looking to brush up on quaternions, eulers, matrices, and vectors as this book is simple and to the point. I think the author did a great job balancing the complexty of the math with simplicity in the book's text. The book goes over what is really the essentials of any 3d math library. ... Read more

7. Fundamentals of Queueing Theory (Wiley Series in Probability and Statistics)
by DonaldGross, Carl M.Harris
list price: $110.00
our price: $110.00
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Asin: 0471170836
Catlog: Book (1998-02-06)
Publisher: Wiley-Interscience
Sales Rank: 353192
Average Customer Review: 5 out of 5 stars
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Book Description

This look at queueing theory stresses the fundamentals of the analytic modeling of queues. It features Excel and Quattro software that allows greater flexibility in the understanding of the nature, sensitivities and responses of waiting- line systems to parameter and environmental changes.

"...this is one of the best books available for use as a textbook for a course and for an applied reference book. Its excellent organizational structure allows quick reference to specific models and its clear presentation coupled with the use of the QTS software solidifies the understanding of the concepts being presented. I highly recommend this book to educators and applied researchers."--IEE Transactions on Operations Engineering ... Read more

Reviews (1)

5-0 out of 5 stars The Classic Queueing Theory Text
Fundamentals of Queueing Theory (third edition) by D. Gross and C. Harris is THE classic queueing text book. It is up-to-date, thorough, rigorous, intuitive, and even fun to read (for the mathematically inclined). This book can be read at different levels, none of them easy. It is intended for an audience of graduate students in operations research, industrial engineering, management science, or mathematics. There are other excellent queueing books out there, but this has to be the overall best seller! Highly recommended. ... Read more

8. The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy
by J.D. Williams
list price: $9.95
our price: $8.96
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Asin: 0486251012
Catlog: Book (1986-05-01)
Publisher: Dover Publications
Sales Rank: 32669
Average Customer Review: 5 out of 5 stars
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Book Description

Highly entertaining text essential for anyone interested in Game Theory. Only basic understanding of arithmetic needed to grasp necessary aspects of two-, three-, four- and larger strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.
... Read more

Reviews (6)

5-0 out of 5 stars Excellent, entertaining introductory text
This is a superlative introduction to a mathematical concept which, with a lesser writer, could be tedious to learn. Williams includes many entertaining and enjoyable story problems, replete with attractive illustrations, that make learning the subject a joy. He takes an inherently interesting topic and makes it easy and fun to learn.

I recommend this book unreservedly.

5-0 out of 5 stars A Fun Introduction to Game Theory
The Compleat Strategyst by J.D. Williams is a wonderful introduction to the ins and outs of game theory. The pace of the primer I found quite reasonable, and the organization is very natural. The Compleat Strategyst begins with the gist (as it should) regarding game matrices and how to interpret them. Williams's discussion then proceeds through 2 x 2 games, 2 x m games, 3 x 3 games, 3 x m games, and so on. Each section contains clever story problems chosen to both re-enforce basic principles and point to potential pitfalls. Also provided are numerous exercises to build the skills necessary to understand game theory.

One of the most enjoyable facets of The Compleat Strategyst is J.D. Williams's entertaining writing style. He seems to know the kind of people reading his book (non-mathematicians who think they might be able to apply game theory to their own work - in my case anyway), and the text is taylored to that audience. In addition, while making the subject matter of game theory accessible strictly through arithmatic, the author provides fair reminders that a great deal of actual mathmatics is being swept beneath the rug.

5-0 out of 5 stars Excellent
I found this book to be an excellent introduction to game theory that doesn't require much mathamatical background beyond simple algebra. It comes complete with theoretical explainations of the game matrix, problems to help sharpen your skills, and strategic stories that fit with a game matrix, to help show how game theory can be applied to real problems. A definite must for anyone who wants to start learning about game theory.

5-0 out of 5 stars Simply excellent
It takes a lot of time to work thru the examples in this book. (I use Excel to speed things up). But it's a great book. First read it at around 1970. Still in love with it.

5-0 out of 5 stars Remembered for years
I first read this book when I was in high school, around 1957. I still remember it today, for a clear, coherent, and funny discussion of game theory, and the statistics controlling the optimum strategy. I hope I can raise a copy of it, since it is out of print! ... Read more

9. Game Theory: A Nontechnical Introduction
by Morton D. Davis
list price: $9.95
our price: $8.96
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Asin: 0486296725
Catlog: Book (1997-07-01)
Publisher: Dover Publications
Sales Rank: 20470
Average Customer Review: 3.89 out of 5 stars
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Book Description

Fascinating, accessible introduction to enormously important intellectual system with numerous applications to social, economic, political problems. Newly revised edition offers overview of game theory, then lucid coverage of the two-person zero-sum game with equilibrium points; the general, two-person zero-sum game; utility theory; other topics. Problems at start of each chapter. Foreword to First Edition by Oskar Morgenstern. Bibliography.
... Read more

Reviews (9)

5-0 out of 5 stars A must for beginner
This is an extremely well written book. It strikes a good balance between a mere book of giving skin deep introductory knowledge of game theory, and a book with too much technical stuff (esp. mathematical proof). The author made a good job almost like Stephen Hawking and Richard Feyman to explain difficult thing with an easy and friendly way. What's more, the author included also many varies paradoxes, theroms from many great leaders in the game theory's field. In beginning of each chapter, the author listed some questions for the reader to think about, before moving forward. I must say this is a very good book for those who are not very sophisticated and advance in mathematics, or as a very first entry for anyone who wants to pursuit and learn game theory.

4-0 out of 5 stars An easy to understand introduction to game theory
I found this book at a used book store and while I generally need little prodding to purchase a math book, in this case a quick glance through the first few pages convinced me to purchase it. Although human emotions are powerful forces in our lives, many of our decisions are still made based on rational thought and perceived benefit. This is the realm of game theory, which is an analysis of decision-making based on the interpretation of rewards and punishment.
The first games examined in this book are the standard ones of two-person zero-sum games, first with and then without equilibrium points. A two-person zero-sum game is one where the winnings of one player must match the losses of the other. In other words, the sum total of value held by the two players is a constant. This is followed by an examination of utility theory, which is a determination of the true value of the rewards and punishments. It is here where emotions and personal preference are the strongest. Something as simple as bragging rights can often have more value than large monetary payments. The next chapter deals with two-person non-zero-sum games, where the total value held by the two players is not a constant. The last chapter deals with n-person games, which are difficult to analyze, but are the most interesting because they are closest to life. Success in n-person games almost always requires the formation of a cooperative, in the sense that there is the potential for a coalition that can dominate everyone else.
What I enjoyed the most about this book was the examples and the problems. At the start of the chapters, there is a set of questions that introduce the material, and they are answered at the end of the chapter. In between, the explanations are clear, with a minimum of formulas. I also enjoyed the sections on the various "games" of voting, such as how does a body of legislators decides how to fund projects when each has their pet project that they want to acquire the funding for. It explains some of the labyrinthine features of the congressional process and why it is possible for a deadlock state to develop.
This is one of the best general introductions to game theory that I have seen, the worked problems take you through the features of the games in a step-by-step manner that is very easy to understand.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

3-0 out of 5 stars Recreational Read
There seems to be a whole cottage industry of books on Game Theory. Not many of them are non-technical, and this is probably the shortest of them. So this is a plus to those with no background and who may not go any further. This book suffers from being slightly out of date.

Game Theory is a subfield not of mathematics but of economics. This despite the fact that one of the greatest mathematicians, Von Neumann, had invented this and that at the advanced level it demands a good deal of higher math. This is a reason why John Nash won the Nobel for economics - and not a Fields Medal (for mathematics).

I think it's dangerous to make life-and-death decisions based on Game Theory. First, it's hardly a real science, only the application of mathematics to social questions. Second, you can easily make an error in your calculations.

This brings to mind Franklin's moral algebra. He advised a friend (Priestly, I think) on how to make intelligent decisions: by dividing the pros and cons into two columns, then giving a value to each in terms of importance (1-10, for example), adding up both columns and comparing the two sums. The larger sum should be the decision. And then he cautioned that real decisions are not necessarily made in this scientific way, although the exercise really sharpens your thinking. At a minimum it forces you to think of all possible pros and cons of a problem. In the end, though, one big pro/con (or two) may decide the matter. And even then, you can't be sure you've made the right decision because maybe you've forgotten something in the arithmetic. Still this is a rational way to think something through, especially on major questions.

The utility of Game Theory is likely to be much less than Franklin's scheme because PEOPLE IN THE REAL WORLD DON'T BOTHER USING IT. Would Roosevelt and Truman have done much better when dealing with Stalin if they had been acquainted with Game Theory? I doubt it, although Game Theory impressed some of the geeks in the Pentagon. (Nor vice versa. Stalin would have just laughed if somebody had tried to "sell" him this academic exercise. He relied on his own judgment.) To this day I have yet to hear that Game Theory is the secret of success of top managers like Jack Welch, Warren Buffett and Sandy Weill.

This book is a good intro to the field and teaches you the basic vocab specialists use. Read it like a book on recreational brainteasers, and you'll have lots of fun. I know I did.

4-0 out of 5 stars Recreational Read
Game Theory is worth a second look, a Nobel Prize having been awarded in 1994 to John Nash, et al. The official Nobel press release specifically cites Von Neumann and Morgenstern as its father. Had both been alive, they might have been the recipients of the prize.

There seems to be a whole cottage industry of books on Game Theory. Not many of them are non-technical, and this is probably the shortest of them. (Another is written by JD Williams: "The Compleat Strategyst" - note the spellings - also from Dover.) So this is a plus to those with no background and who may not go any further. This book suffers from being slightly out of date.

Game Theory is a subfield not of mathematics but of economics. This despite the fact that one of the greatest mathematicians, Von Neumann, had invented this and that at the advanced level it demands a good deal of higher math. This is a reason why John Nash won the Nobel for economics - and not a Fields Medal (for mathematics).

I think it's dangerous to make life-and-death decisions based on Game Theory. First, it's hardly a real science, only the application of mathematics to social questions. Second, you can easily make an error in your calculations.

This brings to mind Franklin's moral algebra. He advised a friend (Priestly, I think) on how to make intelligent decisions: by dividing the pros and cons into two columns, then giving a value to each in terms of importance (1-10, for example), adding up both columns and comparing the two sums. The larger sum should be the decision. And then he cautioned that real decisions are not necessarily made in this scientific way, although the exercise really sharpens your thinking. At a minimum it forces you to think of all possible pros and cons of a problem. In the end, though, one big pro/con (or two) may decide the matter. And even then, you can't be sure you've made the right decision because maybe you've forgotten something in the arithmetic. Still this is a rational way to think something through, especially on major questions.

The utility of Game Theory is likely to much less than Franklin's scheme because PEOPLE IN THE REAL WORLD DON'T BOTHER USING IT. Would Roosevelt and Truman have done much better when dealing with Stalin if they had been acquainted with Game Theory? I doubt it, although Game Theory impressed some of the geeks in the Pentagon. (Nor vice versa. Stalin would have just laughed if somebody had tried to "sell" him this academic exercise. He relied on his own judgment.) To this day I have yet to hear that Game Theory is the secret of success of top managers like Jack Welch, Warren Buffett and Sandy Weill.

Game Theorists themselves disagree on the finer points: Davis in this book points out errors by Anatol Rapoport, for example. This should be enough to give us pause about Game Theory itself.

This book is a good intro to the field and teaches you the basic vocab specialists use. Read it like a book on recreational brainteasers, and you'll have lots of fun. No higher math is required (not even simple algebra) - just a little patience and the motivation to think things through. This is the only low-math intro I know of that covers both 2-person and n-person games of the zero-sum and non-zero-sum varieties in one slim volume.

4-0 out of 5 stars An Introduction to Game Theory
As the name implies, this is a non-technical introduction to a very complex and technical subject. As such, the writer walks a very fine line between making the subject matter understandable to the lay-person and providing scientific support for his arguments. He is able to do this with a mixed level of success.

The first few chapters of the book deal with relatively simple subject matter, two person zero sum games. In these chapters, the author is easily able to explain the concepts and solutions without getting technical. However, as the book progresses, the author grapples with ever more complex problems, such as two person non-zero-sum games and with n-person games. As the problems become more complex, the author's explanations become less well organized and clear. It is obvious that behind the arguments stand solid mathematical reasoning, however since the book tries to avoid mathematics as much as possible, many of the explanations and assumptions remain vague.

Although I was familiar with many of the concepts in the book, this is the first book I have read on game theory. Was it worth it? Absolutely. Although I would have liked to receive more in-depth explanations in many cases, I felt that the book opened a window for me into this fascinating world. I was especially pleased with the many real world examples the author uses to illustrate the wide-ranging applications of game theory. These examples include an application of game theory to the evolution of species; and the use of game theory to determine who holds the power in a political system. More well known concepts, such as the Prisoners' Dilemma, are also comprehensively discussed.

Bottom line, this is a really enjoyable book that covers a very challenging subject. If a non-technical introduction to game theory is what you want, this is the book for you. However, if you are more mathematically inclined or have already read a book or two on the subject, you will probably want to pick up a more advanced book. ... Read more

10. Queueing Networks: Customers, Signals and Product Form Solutions
by XiuliChao, MasakiyoMiyazawa, MichaelPinedo
list price: $176.00
our price: $176.00
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Asin: 0471983098
Catlog: Book (1999-09-15)
Publisher: John Wiley & Sons
Sales Rank: 1415315
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Book Description

Wiley-Interscience Series in Systems and Optimization Queueing Networks Customers, Signals and Product Form Solutions Xiuli Chao, New Jersey Institute of Technology, USA Masakiyo Miyazawa, Science University of Tokyo, Japan Michael Pinedo, New York University, USA 'Mathematically beautiful and elegant yet has much practical application' - Professor Richard Weber The first mathematical analysis of a queueing problem concerned the use of early telephone switches. Since then, emerging technologies such as those in telecommunications and the manufacturing industry have prompted considerable interest and activity in the field. Much of the current research has been enabled by recent, rapid advances in computer technology making large scale simulations and complex approximations possible. Today, queueing systems play an integral role in the performance evaluation and optimization of computer, communication. manufacturing and transportation systems. Includes:
* Discussion on the fundamental structures of queueing network models
* The latest developments in the field
* Thorough examination of numerous applications
* Exercises at the end of each chapter
* Coverage of queueing networks with signals
* Discussion of future research developments
With the advances in information technology, many networks have, in addition to conventional jobs, signals and messages circulating throughout the system. A signal carries information and instructions and may trigger complex simultaneous events. The objective of this book is to present, in a unified framework, the latest developments in queueing networks with signals, After introducing the foundations in the first four chapters, Chapters 5 through to 8 cover a number of different queueing network models with various features. Chapters 9 to 11 focus on more fundamental structures of queueing networks and Chapter 12 presents a framework for discrete time queueing network models. The text is illustrated throughout with numerous examples. Graduate students in operations research, computer science, electrical engineering and applied mathematics will find this text accessible and invaluable. An essential reference for operation researchers and computer scientists working on queueing problems in computing, manufacturing and communications networks.
... Read more

11. The Mathematics of Games and Gambling (New Mathematical Library)
by Edward Packel
list price: $24.95
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Asin: 088385628X
Catlog: Book (1996-09-05)
Publisher: The Mathematical Association of America
Sales Rank: 52576
Average Customer Review: 4.5 out of 5 stars
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Book Description

You can't lose with this MAA Book Prize winner if you want to see how mathematics can be used to analyze games of chance and skill. Roulette, craps, blackjack, backgammon, poker, bridge, lotteries and horse races are considered here in a way that reveals their mathematical aspects. The tools used include probability, expectation, and game theory. No prerequisites are needed beyond high school algebra. No book can guarantee good luck, but this book will show you what determines the best bet in a game of chance or the optimal strategy in a strategic game.Besides being an excellent supplement to a course on probability and good bed-side reading, this book's treatment of lotteries should save the reader some money. ... Read more

Reviews (2)

5-0 out of 5 stars Will help you win?
This is one of the most entertaining books on the subject of game theory! Highly recommended. Of course, you may not win all the time in any gambling games but if after studying it, you will have a sense of how it works! THat is it!

4-0 out of 5 stars Basic, yet thorough intro to the theory of games of chance
When I was teaching full-time in the '80s, the math topic that students found most interesting was the analysis of gambling. One student in particular had written a program that analyzed the past history of racing greyhounds in an attempt to increase his odds of winning at the dog track. The students were also the most attentive in class when I was working through an analysis of either casino games or the state run lotteries. We held several discussions on various ways to "beat" the games that were suggested by the students or explained in class. I received and answered many questions about the odds of winning in many scenarios, sometimes to the disappointment and disbelief of the person asking the question. From now on, I will direct students with such questions to this book if they find my answers unsatisfactory.
It is a brief, yet thorough analysis of the mathematical foundations of some basic board and casino games. Problems for further testing and study are given at the end of most sections, so it is possible to use it as a textbook in short courses in basic probability theory. The level of difficulty is consistent with that of a beginning course, and the only mathematical prerequisites are the most basic of algebraic operations.
Gambling is an activity that will continue to be a part of the human experience as long as humans have their present form. To many, it is an activity of addiction, to others one of recreation and to mathematicians it can be both. I fall in the latter category, as I often point out to people how their opinions about the possibility of success are exactly what the gambling companies want them to be. This book is an excellent description of how the games work and how billions are made by being on the right side of slightly favorable odds. ... Read more

12. The Essential John Nash
by John Nash
list price: $34.95
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Asin: 0691095272
Catlog: Book (2001-11-19)
Publisher: Princeton University Press
Sales Rank: 55481
Average Customer Review: 4.5 out of 5 stars
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Book Description

When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive and well. Since then, Sylvia Nasar's celebrated biography, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics, in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.

From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.

In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.

The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from. ... Read more

Reviews (12)

5-0 out of 5 stars Fascinating Reading
Even without the Nobel Prize for Economics, the outstanding movie by Ron Howard ("A Beautiful Mind"), or the exceptional biography by Sylvia Nasar (also "A Beautiful Mind"), Professor John Nash would a legend. While cursed with severe mental illness, Dr. Nash was and is an extraordinary man. His contributions to game theory were so ahead of their time it took over 30 years for economists and business leaders to apply them fully. When they were applied, they advanced everything from international trade talks and arms control treaties, to radio frequency auctions and the study of evolutionary biology. Dr. Nash's work has had a profound, highly practical impact on negotiation and decision making throughout business and government. He created a path toward win-win solutions to complex, multi-party agreements.

This book is largely a collection of Dr. Nash's own writings, each a significant contribution to mathematics or economics. Nash's papers are thoughtfully introduced and explained - thankfully so given the complexity of Nash's writings. Also included is Nash's own touching and revealing autobiography.

The result is a compelling glimpse inside the thought processes of a genius - a beautiful mind indeed. Thanks to Harold Kuhn and Sylvia Nasar for pulling this wonderful collection together.

5-0 out of 5 stars An excellent compilation
Having written about the life of the mathematician John Nash in the excellent biography "A Beautiful Mind", Sylvia Nasar teams up with the mathematician Harold W. Kuhn to produce a book that introduces the mathematical contributions of Nash, something that was done only from a "popular" point of view in Nasar's biography. For those who have the background, this book is a fine overview of just what won Nash acclaim in the mathematical community, and won him a Nobel Prize in economics.

It is always easy to dismiss ideas as trivial after they have been discovered and have been put into print. This is apparently what John von Neumann did after discussing with Nash his ideas on noncooperative games, dismissing his ideas as a mere "fixed point theorem". At the time of course, the only game-theoretic ideas that had any influence were those of von Neumann and his collaborator, the Princeton economist Oskar Morgenstern. The rejection of ideas by those whose who hold different ones is not uncommon in science and mathematics, and, from von Neumann's point of view at the time, he did not have the advantage that we do of examining the impact that Nash's ideas would have on economics and many other fields of endeavor. Therefore, von Neumann was somewhat justified, although not by a large measure, in dismissing what Nash was proposing. Nash's thesis was relatively short compared to the size on the average of Phd theses, but it has been applied to many areas, a lot of these listed in this book, and others that are not, such as QoS provisioning in telecommunication and packet networks. The thesis is very readable, and employs a few ideas from algebraic topology, such as the Brouwer fixed point theorem.

The paper on real algebraic manifolds though is more formidable, and will require a solid background in differential geometry and algebraic geometry. However, from a modern point of view the paper is very readable, and is far from the sheaf and scheme-theoretic points of view that now dominate algebraic geometry. It is interesting that Nash was able to prove what he did with the concepts he used. The result could be characterized loosely as a representation theory employing algebraic analytic functions. These functions are defined on a closed analytic manifold and serve as well-behaved imbedding functions for the manifold, which is itself analytic and closed. These manifolds have been called 'Nash manifolds' in the literature, and have been studied extensively by a number of mathematicians.

I first heard about John Nash by taking a course in algebraic topology and characteristic classes in graduate school. The instructor was discussing the imbedding problem for Riemannian manifolds, and mentioned that Nash was responsible for one of the major results in this area. His contribution is included in this book, and is the longest chapter therein. Here again, the language and flow of Nash's proof is very understandable. This is another example of the difference in the way mathematicians wrote back then versus the way they do now. Nash and other mathematicians of his time were more 'wordy' in their presentations, and this makes the reading of their works much more palatable. This is to be contrasted with the concisness and economy of thought expressed in modern papers on mathematics. These papers frequently employ a considerable amount of technical machinery, and thus the underlying conceptual foundations are masked. Nash explains what he is going to do before he does it, and this serves to motivate the constructions that he employs. His presentation is so good that one can read it and not have to ask anyone for assistance in the understanding of it. This is the way all mathematical papers should be written, so as to alleviate any dependence on an 'oral tradition' in mathematical developments.

Nash's proof illuminates nicely just what happens to the derivatives of a function when the smoothing operation is applied. The smoothing operator consists of essentially of extending a function to Euclidean n-space, applying a convolution operator to the extended function, and then restricting the result to the given manifold. Nash gives an intuitive picture of this smoothing operator as a frequency filter, passing without attenuation all frequencies below a certain parameter, omitting all frequencies above twice this parameter, and acting as a variable attenuator between these two, resulting in infinitely smooth function of frequency.

The next stage of the proof of the imbedding theorem is more tedious, and consists of using the smoothing operator and what Nash calls 'feed-back' to construct a 'perturbation device' in order to study the rate of change of the metric induced by the imbedding. Nash's description of the perturbation process is excellent, again for its clarity in motivating what he is going to do. The feed-back mechanism allows him to get a handle of the error term in the infinitesimal perturbation, isolating the smoother parts first, and handling the more difficult parts later. Nash reduces the perturbation process to a collection of integral equations, and then proves the existence of solutions to these equations. A covariant symmetric tensor results from these endeavors, which is CK-smooth for k greater than or equal to 3, and which represents the change in the metric induced by the imbedding of the manifold. The imbedding problem is then solved for compact manifolds by proving that only infinitesimal changes in the metric are needed. The non-compact case is treated by reducing it to the compact case. The price paid for this strategy is a weakening of the bound on the required dimension of the Eucliden imbedding space.

The last chapter concerns Nash's contribution to nonlinear partial differential equations. I did not read this chapter, so I will omit its review.

5-0 out of 5 stars Good Collection of Nash Writings!
I only rate books that I really enjoy reading. While this one has some techy chapters, readers without a strong math background can still enjoy it.

Professor Nash's story was brought to life by the movie, this book shows why. One day his manifold theory will rule! ;)

5-0 out of 5 stars excellent
Personally, I found this book to be very interestring. The proofs and ideas are presented in clear and non-rigomorphic fashion. One is able to read the works of Nash in the way he himself presented them, and hopefully appropriate some mental strategies used by this genius. There is much that goes on behind the scene of creation of proofs. I think mathematicians of today would greatly benefit from availability of larger number of books which would contain the mathematical works in the way they were originally presented. This is certainly a major step in that direction.

5-0 out of 5 stars A Most Welcome Mathematical Banquet
I can't begin to express how deeply satisfying it was to peruse these papers by John Nash. You almost felt you were right there at his side, as he penned them.

There is even something in the book for non-mathematical types: Sylvia Nasar's Introduction and the autobiographical essay (Chapter Two). But for me the greatest interest resided in the remaining chapters: 4-11.

Of these, I particularly enjoyed reading the original presentation of Nash's Thesis on 'Non-Cooperative Games' (Chapter 6), and was fascinated not only with the air-tight logic of his proofs, but the use of hand written-in symbols.

Of course, Chapter 7 is just the re-hashing of Ch. 6, but in proper type-set form, rather than Nash's original script. But - give me the former any day! Reading the original form and format almost made me feel like Nash's Thesis aupervisor, including the same excitement of a new discovery!

Chapter 8 'Two person Cooperative Games' nicely extends the mathematical basis to cover this species of interaction.(And in many ways, people will find the cooperative game model easier to understand than the non-cooperative).

Chapter 9 is important because it delves into the issue of parallel control, and logical functions such as used in high speed digital computers. This chapter was of much interest to me since particular aspects of parallel control figured in my own model of consciousness - recently presented in Chapter Five of my book, 'The Atheist's Handbook to Modern Materialism'. Astute readers who read both books will quickly see the analog between the Schematic of Logical Unit Function (p. 122) and my own Figure 5-13 ('Development of Neural Assemblies', p. 156).

I enjoyed Chapter 10, 'Real Algebraic Manifolds' because of my ongoing interest in Algebraic Topology, and especially homology and homotopy theory. In his chapter, Nash presents a cornucopia of methods for representation, which I am still playing with for different manifolds.

Chapter 11, 'The Imbedding Problem for Riemannian Manifolds', is a delight for anyone familiar with Einstein's General Relativity, or even differential geometry. When you read through this chapter, you also will understand why Nash is still very interested (and involved) in research to do with general relativity and cosmology. Particularly fun for me was his section on 'Smoothing of Tensors' (p. 163) and 'Derivative Size Concept for Tensors' (p. 164).

Chapter 12, 'Continuity of Solutions of Parabolic and Elliptic Equations' is like 'dessert' for anyone who is intensely interested (as I am) in modular functions, which themselves are related intimately to elliptic equations.

In short, I think this book has something for both mathematicians and non-math types alike. Obviously, the former are likely to get more out of it, so the question the latter group must ask is whether the purchase is worth satiating their curiosity about Nash.

I know how I would answer, even if I couldn't tell a derivative from a differential. However, this book can be read on all kinds of levels, and that's the beauty of it. ... Read more

13. Numerical Optimization
by Jorge Nocedal, Stephen J. Wright
list price: $79.95
our price: $67.96
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Asin: 0387987932
Catlog: Book (1999-08-27)
Publisher: Springer-Verlag
Sales Rank: 149937
Average Customer Review: 4.5 out of 5 stars
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Book Description

NUMERICAL OPTIMIZATION presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available.

Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the area.

Above all, the authors have strived to produce a text that is pleasant to read, informative and rigorous--one that reveals both the beautiful nature of the discipline and its practical side. ... Read more

Reviews (2)

5-0 out of 5 stars Teaches good mathematical programming techniques
The book does a very good job in teaching non-discrete mathematical programming techniques. But, it is not an introductory book. The reader is supposed to know linear algebra and numerical analysis to a certain extent. Most of the modern techniques are presented, but the layout is a little chaotic- the sequence of subjects could be made better. So, I would have preferred to give it 4.5 stars (which is impossible). However, that does not take away the fact that the book is excellent. I have used it primarily for modelling financial portfolios, and I am sure it can be used as a guide for other applications.

Conclusion: A little difficult, but well worth the time and money involved

4-0 out of 5 stars Nice but could be better!
This book by Nocedal and Wright has several attractive features. For one, it is probably the most "state-of-the-art" of the existing texts in optimization and as such covers most of the modern methods. It also has a nice section on LP (simplex as well as interior point methods) for someone interested in a course on optimization as opposed to NONLINEAR optimization (which is what I was looking for). Another strength is that it covers many of the algebra-related details very well. My only major complaint is that it seems to not get into any of the methods designed specifically for convex programs - these while admittedly less general are often very powerful. For example, there is NO mention even of Geometric Programming which has wide application in design. The convex simplex method also isn't mentioned anywhere. Finally,I wonder why there is no mention of the generalized reduced gradient (GRG) method.

All in all, a good book to own I think... ... Read more

14. On Numbers and Games
by John Horton Conway
list price: $45.00
our price: $45.00
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Asin: 1568811276
Catlog: Book (2000-12-01)
Publisher: AK Peters, Ltd.
Sales Rank: 70684
Average Customer Review: 5 out of 5 stars
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Book Description

ONAG, as the book is known, is one of those rare publications that sprang to life in amoment of creative energy and has remained influential for over a quarter of a century. Still in highdemand, it is being republished with some adjustments and corrections. The original motivation forwriting the book was an attempt to understand the relation between the theories of transfinite numbers andmathematical games. By defining numbers as the strengths of positions in certain games, the authorarrives at a new class, the surreal numbers (so named by Donald Knuth) that includes at the same time thereal numbers and the ordinal numbers.

This new edition ends with an epilogue that sets the stage for further research on surreal numbers. Thebook is a must-have for all readers with a serious interest in the mathematical foundations of gamestrategies. ... Read more

Reviews (3)

5-0 out of 5 stars Math geek heaven
Boy, you wanna talk about your _cool_ books. I read this one twenty years ago and never quite got over it. Georg Cantor sure opened a can of worms with all that infinity stuff.

John Horton Conway is probably best known as the creator/discoverer of the computer game called "Life," with which he re-founded the entire field of cellular automata. What he does in this book is the _other_ thing he's best known for: he shows how to construct the "surreal numbers" (they were actually named by Donald Knuth).

Conway's method employs something like Dedekind cuts (the objects Richard Dedekind used to construct the real numbers from the rationals), but more general and much more powerful. Conway starts with the empty set and proceeds to construct the entire system of surreals, conjuring them forth from the void using a handful of recursive rules.

The idea is that we imagine numbers created on successive "days". On the first day, there's 0; on the next, -1 and +1; on the next, 2, 1/2, -1/2, and -2; on the next, 3, 3/4, 1/4, -1/4, -3/4, and -3; and so on. In the first countably-infinite round, we get all the numbers that can be written as a fraction whose denominator is a power of two (including, obviously, all the whole numbers). We can get as close to any other real number as we like, but they haven't actually been created yet at this point.

But we're just getting started. Once we get out past the first infinity, things really get weird. By the time we're through, which technically is "never," Conway's method has generated not only all the real numbers but way, way, way more besides (including more infinities than you've ever dreamed of). His system is so powerful that it includes the "hyperreal" numbers (infinitesimals and such) that emerge (by a very different route, of course) from Abraham Robinson's nonstandard analysis as a trivial special case.

So there's a lot here to get your mind around, and it's a lot of fun for readers who like to watch numbers being created out of nothing. But wait -- there's more.

See, the _full_ title of the book includes not only "numbers" but also "games". And that's the rest of the story. Conway noticed that in the board game of Go, there were certain patterns in the endgames such that each "game" looked like it could be constructed out of smaller "games". It turns out that something similar is true of all games that have certain properties, and that his surreal numbers tie into such games very nicely; "numbers" (and their generalizations) represent strategies in those games. So in the remainder of the book Conway spells this stuff out and revolutionizes the subject of game theory while he's at it.

Well, there must be maybe two or three people in the world to whom this all sounds very cool and yet who haven't already heard of this book. To you I say: read it before you die, and see how God created math.

5-0 out of 5 stars A very dense collection of original ideas
We all think we know numbers, and yet every once in awhile something comes along that makes us realize that we actually know very little. I am not talking about facts such as whether a specific large number is prime, but about the fundamental definition of what a number is. The appearance of the surreal numbers is one of those mathematical equivalents of a whack on the side of the head. Suddenly, numbers are defined as the strengths of positions in certain games, something that is at first strange, but it turns out that the class of objects defined this way includes the real and ordinal numbers. It certainly is different, and I had to read the first thirty pages of the book three times before I felt that I truly grasped the concepts behind the definition of the surreal numbers.
From that things move more smoothly. As I read through the book, it was easy to get the impression that most of life can be described as a game, where our day-to-day status in the community can be described as a dynamic set of surreal numbers. I often wondered if that may be an effective approach for artificial intelligence work, as it certainly seems that surreal numbers can be used to model almost any dynamic situation. Furthermore, effective game playing is nothing more than effective decision making.
There are many significant ideas in the book, at times you stop and start mentally jumping through different scenarios, as in "What would be the change if this rule is added, dropped or altered?" It seems that if you took that approach, several lifetimes could be spent in exploring all the possibilities. I have read many books and this one is most likely the densest carrier of new ideas that I have ever encountered.

5-0 out of 5 stars A Truly Amazing Piece of Work
Conway deals with a certain type of game: games with no element of chance (no dice), the players have complete knowledge about the state of the game (no hidden hand signs like scissors-paper-stone) and where the last player to move wins (though that can be stretched to include Dots and Boxes and endgames from Go - though not in this book).

Conway defines a bunch of mathematical objects. He defines mathematical operations on these objects such as addition and multiplication. The whole work looks suspiciously like a way to define the integers and arithmetic starting from set theory. But we soon see that his construction allows for all sorts of things beyond just integers. We quickly get to fractions and irrationals and we see that he has given us a wonderful new way to construct the real line. Then we discover infinities and all sorts of weird new numbers called nimbers that have fascinating properties.

It all looks a bit abstract until you get to part two (well, he actually starts at part zero so I mean part one). At this point you discover that these objects are in fact positions in games and that the ordinary everyday numbers we know so well are in fact special types of games. Ordinary operations like addition, subtraction and comparison turn out to have interpretations that are game theoretical. So in fact Conway has found a whole new way to think about numbers that is beautiful and completely different to the standard constructions. Even better, you can use this new found knowledge to find ways to win at a whole lot of games.

It's not every day that someone can make a connection like this between two separate branches of mathematics so I consider this book to be nothing less than a work of genius.

BTW This is the Conway who invented (the cellular automaton) the Game of Life and came up with the Monstrous Moonshine Conjectures (whose proof by Borcherds recently won the Fields Medal in mathematics). ... Read more

15. Game Theory and the Social Contract, Vol. 2: Just Playing (Economic Learning and Social Evolution)
by Ken Binmore
list price: $75.00
our price: $75.00
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Asin: 0262024446
Catlog: Book (1998-07-17)
Publisher: The MIT Press
Sales Rank: 738211
Average Customer Review: 5 out of 5 stars
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Book Description

"Ken Binmore's Game Theory and the Social Contract is the most important work in social philosophy since John Rawls' Theory of Justice. It is highly original, insightful, and will be a focal point for social theory." -- Brian Skyrms, Distinguished Professor of Philosophy and Professor of Economics, University of California, Irvine

In Volume 1 of Game Theory and the Social Contract, Ken Binmore restated the problems of moral and political philosophy in the language of game theory. In Volume 2, Just Playing, he unveils his own controversial theory, which abandons the metaphysics of Immanuel Kant for the naturalistic approach to morality of David Hume. According to this viewpoint, a fairness norm is a convention that evolved to coordinate behavior on an equilibrium of a society's Game of Life. This approach allows Binmore to mount an evolutionary defense of Rawls's original position that escapes the utilitarian conclusions that follow when orthodox reasoning is applied with the traditional assumptions. Using ideas borrowed from the theory of bargaining and repeated games, Binmore is led instead to a form of egalitarianism that vindicates the intuitions that led Rawls to write his Theory of Justice.

Written for an interdisciplinary audience, Just Playing offers a panoramic tour through a range of new and disturbing insights that game theory brings to anthropology, biology, economics, philosophy, and psychology. It is essential reading for anyone who thinks it likely that ethics evolved along with the human species. ... Read more

Reviews (2)

5-0 out of 5 stars Important Contribution to Political Philosophy
Binmore treats ethics not as a system of rules justified by Reason, but as by contrast, ethics the scientific study of how humans behave and think. Binmore reports extensively on contemporary ethnographies of hunter-gatherer societies, believing that such societies mirror the social and material conditions the human race faced during its formative period as a species. Such societies have no division of labor except for gender, and are politically egalitarian, decision-making power being quite equally distributed among the adult males of the community. Binmore infers that fairness norms must be self-enforcing, and cannot depend on a hierarchical leader (a "philosopher-king") to enforce ethical principals. Moreover, since a division of labor (except for gender) is absent, deliberations in such groups approximate the `original position.'

Binmore thus offers us a "coevolution of genes and culture" in which the acceptance of original position moral arguments is written into our genes, but the cultural content depends on local environmental conditions and random variation. Again drawing on the ethnographic literature, Binmore focuses on food sharing as the most important rule of justice to be decided by a foraging group. In foraging societies, high variance foodstuffs such as meat are equally shared, irrespective of who made the kill. Equal sharing is thus a moral rule justified by reasoning from the original position of hunters who do not know exactly which among them will be lucky or skilled.

Binmore uses evolutionary game theory to analyze social interactions. This adds a welcome degree of clarity to ethical reasoning. Indeed, Binmore is quite clear that all of his substantive results depend on the plausibility of the game theoretic models he presents and analyzes.

While fairness norms are biologically determined for Binmore, the players in Binmore's games are rational self-interested agents. Thus all of the results of two-person game theory based on the rational actor model can be deployed in analyzing social justice. It follows in particular that "[i]n a well-ordered society, each citizen honors the social contract because it is in his own self-interest to do so, provided that enough of his fellow citizens do the same." (5) There is no sense in which moral behavior is opposed to self-interested behavior. Moreover, since players do not behave ethically in bargaining, there is no sense in which the institutions resulting from their bargaining have any abstract normative standing. "Evolutionists simply seek to understand," says Binmore, "why some types of human organization survive better than others.... evolutionary ethics offers no authority whatsoever to those who wish to claim that some moral systems are somehow intrinsically superior to others.' (179)

Different societies can thus embrace different institutions because comparisons in the original position depend on `empathetic preferences' that are culturally specific. It is in part for this reason that Binmore calls himself a `whig,' by which he means a moderate progressive, not seduced by the grand visions of a totally alternative society as proposed by the Left and the Right. The latter two, he claims, make social judgments in a universal, ahistorical manner that have nothing to do with the actual fairness processes in real societies.

Just Playing is an important and welcome contribution to the literature. The book does, however, have some faults. The most salient is that crucial analytical material and discursive asides jumbled together. One must read the whole book, and make numerous references back and forth, to understand the basic argument. Moreover, the book is intended for a general audience interested in political philosophy, yet even professional economists will find the analytical parts difficult to follow.

Another problem is that Binmore uses evolutionary game theory where it suits him, but abandons it when it does not. For instance, while Binmore uses naturalism to justify the assertion that Homo sapiens is genetically programed to accept the original position, but he gives no empirical evidence that this is in fact the case. Moreover, it is implausible that evolution imprinted us with an original position orientation, but in no other way affected our moral behavior, so that the assumption of Homo economicus remains valid for bargaining purposes. Laboratory experiments reveal forms of prosocial behavior (e.g., rejecting `unfair' offers in an ultimatum game, or punishing free riders in a public goods game) that relate directly to questions of justice and fairness, yet contradict the Homo economicus model. The notion that human sociality can be explained by `enlightened self-interest,' even when accompanied by respect for the original position, will not likely survive a close study of the evidence (See my book Game Theory Evolving, Princeton University Press, 2000).

5-0 out of 5 stars Upgrading Rawls' "Theory of Justice"
In his exciting theory of the social contract Ken Binmore takes 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. ... Read more

16. Dynamic Optimization
by Morton I. Kamien, Nancy L. Schwartz
list price: $114.95
our price: $114.95
(price subject to change: see help)
Asin: 0444016090
Catlog: Book (1991-10-01)
Publisher: Elsevier Science
Sales Rank: 411206
Average Customer Review: 4.5 out of 5 stars
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Book Description

Hardbound. The long awaited second edition of Dynamic Optimization is now available. Clear exposition and numerous worked examples made the first edition the premier text on this subject. Now, the new edition is expanded and updated to include essential coverage of current developments on differential games, especially as they apply to important economic questions; new developments in comparative dynamics; and new material on optimal control with integral state equations.

The second edition of Dynamic Optimization provides expert coverage on:- methods of calculus of variations - optimal control - continuous dynamic programming - stochastic optimal control -differential games. The authors also include appendices on static optimization and on differential games.

Now in its new updated and expanded edition, Dynamic Optimization is, more than ever, the optimum choice for graduate and advanced undergraduate courses in economics, mathem ... Read more

Reviews (2)

4-0 out of 5 stars Chiang's book is best.
This book is decent, but I think that Chiang book is better that this book, I recommend "Elements of Dynamic Optimization" from Alpha Chiang (ISBN: 157766096X), it's better.

5-0 out of 5 stars A must book for every serious economics student
There is no doubt that to master in advanced economics one should have a firm grasp on mathematical tools. Kamien and Schwartz's Dynamiz Optimization is the perfect book to this end. Actually it deserves a rating more than five stars. ... Read more

17. A First Course in Optimization Theory
by Rangarajan K. Sundaram
list price: $34.99
our price: $25.54
(price subject to change: see help)
Asin: 0521497701
Catlog: Book (1996-06-13)
Publisher: Cambridge University Press
Sales Rank: 64912
Average Customer Review: 4.4 out of 5 stars
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Book Description

This book introduces students to optimization theory and its use in economics and allied disciplines.The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified.The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming.A preliminary chapter and three appendices are designed to keep the book mathematically self-contained. ... Read more

Reviews (5)

5-0 out of 5 stars The title says it all
A first course in Optimization theory - that is what the book is. The target audience is those who are inetersted in the theory of optimization. Some familiarity with Mathematical Analysis and Matrix Algebra would be helpful; however the first chapter lays the mathematical foundation and a careful reading would enable the reader to tackle the rest of the book.

Previous reviews have made a chapter by chapter analysis of the book and hence I will just highlight some of the things I liked about the approach used by the author. Whenever a theorem is stated different examples are given to emphasize the points. For example when stating the Lagrange Theorem and Kuhn-Tucker theorem the author points out when the theorems fail and gives detailed examples to illustrate the ideas. The author often draws from examples in finance to illustrate the practical importance of the theory. The one I liked most was how a cost minimization problem was solved by reducing the solution space to a compact space and then applying the Weierstrass theorem. The author also shows how some of the "cookbook" procedures really work and warns the readers against potential pitfalls in applying such procedures. If you are planning to study optimization theory and are looking for a good entry point into the subject this book is for you.

4-0 out of 5 stars Good introduction to the field of optimization
This book gives a nice introduction to the theory of optimization from a purely mathematical standpoint. The computational and algorithmic aspects of the subject are not treated, with emphasis instead placed on existencetheorems for various optimization problems. The author does an effective job of detailing the mathematical formalism needed in optimization theory. After a brief review of background mathematics in the first chapter, the author outlines the objectives of optimization theory in Chapter Two. He also gives some examples of optimization problems, such as utility maximization, expenditure minimization, profit maximization, cost minimization, and portfolio choice. All of these examples are extremely important in industrial, logistical, and financial applications. The author is also careful in this chapter to outline his intentions in later chapters, namely, that of finding the existence of solutions to optimization problems, and also in the characterization of the set of optimal points. The existence question is outlined in Chapter Three using only elementary calculus, and the Weierstrass theorem is proved. Necessary conditions for unconstrained optima are examined in the next chapter, again using only elementary calculus and linear algebra. Lagrange multipliers and how they are used in constrained optimization problems are effectively discussed in Chapter 5. To discuss how optimization problems vary with a set of parameters, in particular if they vary continuously with the set of parameters, the author introduces the concept of a corespondence. This is essentially a map that assigns sets to points. His discussion of upper and lower-semicontinuity is very clear and I think one of the best presentations given at this level. He then proves a maximum theorem, showing that parametrized optimization problems can have continuous solutions under certain conditions. A game-theoretic application follows along with statements, but not proofs, of the Kakutani and Brouwer Fixed Point theorems. The author introduces an order relation on the parameter space and discusses parametric monotonicity in the next chapter. Again a game theory application is given along with a statement (but not a proof) of the Tarski Fixed Point theorem. The last two chapters cover dynamic programming and these are the most interesting chapters of the book. It is here that the author makes the connection with more advanced treatments of optimization theory, via Banach spaces and nonlinear functional analysis. With further reading in real analysis and topology, readers will be well on their way to understanding more advanced treatments of optimization theory that use nonlinear functional analysis and differential topology.

3-0 out of 5 stars Unless you're into theory, this book is NOT for you
I'm a applied mathematician with over 40 quarter hours of theoretical math under my belt, and frankly I feel this book would be rough going for anyone who does not have a rigid math theory background. In other words, if you're not a graduate student or a theoretical practioner in the field of optimization, this is NOT the book for you (most likely). But I also have two other problems with this book.

First, it is touted to have numerious examples of both theory and applications. Theory, as I mentioned above, it has in abundance. But it is very thin on practical applications.

Second, this book has numerious problems at the ends of the chapters WITH NONE OF THEM WORKED OUT! Frankly, I'm not really interested in paying almost $30 for a paperback book that is unfinished.

Perhaps I was expecting much more than what I got after reading the glowing reviews above; and in hindsight, I really should have paid more attention to the title as "Theory" is indeed the operative word. My irritation is not in the book itself, as the author states in his forward that he is writing a book aimed the graduate school set; but is aimed at the reviewers above which led me to think that this text was much wider based than it turned out to be.

5-0 out of 5 stars Great book and an even greater value
This book was organized and written with perfection. The explanations are remarkable and the "cookbook" procedures for Lagrange and K-T methods were great. I especially admired the fact that the author actually mentioned how these procedures could fail to yield an optimized value. This is worthwhile in today's university mathematics where one is simply taught to plug numbers into formulae and algorithms to get the desired answer. The book also slants towards optimization problems in economic theory as well as other disciplines. Finally, in an age when textbooks can easily run over $100, it was nice to see this book, filled with a wealth of information, so moderately priced.

5-0 out of 5 stars Excellent book for PhD students in Operations Management
This is an excellent book for anybody interested in non-linear optimization within economics framework. The book is self-contained and includes all the basic theory one needs to know to understand optimization. To my knowledge, this is the only book merging non-linear optimization with game theory and such concepts as supermodularity and parametric monotonicity. ... Read more

18. Winning Ways for Your Mathematical Plays, Vol. 3
by Elwyn R. Berlekamp, John Conway, Richard Guy, John Horton Conway, Richard K. Guy
list price: $49.00
our price: $49.00
(price subject to change: see help)
Asin: 1568811438
Catlog: Book (2003-09-01)
Publisher: AK Peters, Ltd.
Sales Rank: 125335
Average Customer Review: 5 out of 5 stars
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Book Description

In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the second edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure.

In Volume 3, the authors examine Games played in Clubs, giving case studies for coing and paper-and-pencil games, such as Dots-and-Boxes and Nimstring. ... Read more

Reviews (1)

5-0 out of 5 stars Enjoyable discussion of many interesting games
Starting with Hackenbush (thanks to Groucho Marx) this book describes and analyzes a great many interesting games. While the authors are mathematicians, and there is mathematics involved, much of the discussion can be followed by the lay reader. ... Read more

19. The Theory of Learning in Games (Economic Learning and Social Evolution)
by Drew Fudenberg, David K. Levine
list price: $45.00
our price: $38.70
(price subject to change: see help)
Asin: 0262061945
Catlog: Book (1998-05-22)
Publisher: The MIT Press
Sales Rank: 392601
Average Customer Review: 4 out of 5 stars
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Book Description

"This book collects the essential existing results in the fast-paced field of learning and evolutionary game theory together with new work by two leaders in the field. It will be essential to anyone doing theoretical work on learning and games or using evoultionary game theory in applied work." -- Larry Samuelson, Antoine Augustin Cournot Professor of Economics, University of Wisconsin

In economics, most noncooperative game theory has focused on equilibrium in games, especially Nash equilibrium and its refinements. The traditional explanation for when and why equilibrium arises is that it results from analysis and introspection by the players in a situation where the rules of the game, the rationality of the players, and the players' payoff functions are all common knowledge. Both conceptually and empirically, this theory has many problems.

In The Theory of Learning in Games Drew Fudenberg and David Levine develop an alternative explanation that equilibrium arises as the long-run outcome of a process in which less than fully rational players grope for optimality over time. The models they explore provide a foundation for equilibrium theory and suggest useful ways for economists to evaluate and modify traditional equilibrium concepts. ... Read more

Reviews (2)

4-0 out of 5 stars Learning Learning in Games
An excellent treatise on some important work in the theory of learning in games. Fudenberg and Levine provide a good coverage of standard myopic play dynamics with a special emphasis on ficticious play and replicator dynamics. I particularly liked the sections going through the Kandori, Mailath and Rob (1993) model as well as Young (1993) on the evolution of convention.

The treatments of dynamic systems analysis, elementary game theory, stochastic approximation theory, etc., are necessarily short. The appendices do not suffice for a reader without a reasonable background.

Nonetheless an essential read for anybody doing serious work in learning, or wanting to know what all the fuss is about.

4-0 out of 5 stars Good book
During the work on my master thesis ("Learning in strategic games") i bought several books about the topic. This is the one of them. Chapters 1 and 2 (Introduction, Fictitious Play) are really good introduction into the subject. The following chapters evolve the theory further giving some good ideas for practical implementation (I was writing a C program which had to be able to play the game and to learn). I would recommend this book to anyone interested in relatively new field - Learning in games. ... Read more

20. Winning Ways for Your Mathematical Plays Volume 2
by Elwyn Berlekamp, John H. Conway, Richard K. Guy, Elwyn R. Berlekamp, John Conway, Richard Guy
list price: $39.00
our price: $39.00
(price subject to change: see help)
Asin: 156881142X
Catlog: Book (2003-01-01)
Publisher: AK Peters, Ltd.
Sales Rank: 76670
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Book Description

In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure.

In Volume 2, the authors have a Change of Heart, bending the rules established in Volume 1 to apply them to games such as Cut-cake and Loopy Hackenbush.

From the Table of Contents:
If You Can't Beat 'Em, Join 'Em
Hot Bottles Followed by Cold Wars
Games Infinite and Indefinite
Games Eternal--Games Entailed
Survival in the Lost World ... Read more

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