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Covering both noncooperative and cooperative games, this comprehensive introduction to game theory also includes some advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences to being an authoritative reference for researchers.
- Sales Rank: #317080 in Books
- Published on: 2013-05-06
- Original language: English
- Number of items: 1
- Dimensions: 9.69" h x 1.97" w x 7.44" l, 4.95 pounds
- Binding: Hardcover
- 1003 pages
Review
'This is the book for which the world has been waiting for decades: a definitive, comprehensive account of the mathematical theory of games, by three of the world's biggest experts on the subject. Rigorous yet eminently readable, deep yet comprehensible, replete with a large variety of important real-world applications, it will remain the standard reference in game theory for a very long time.' Robert Aumann, Nobel Laureate in Economics, The Hebrew University of Jerusalem
'Without any sacrifice on the depth or the clarity of the exposition, this book is amazing in its breadth of coverage of the important ideas of game theory. It covers classical game theory, including utility theory, equilibrium refinements and belief hierarchies; classical cooperative game theory, including the core, Shapley value, bargaining set and nucleolus; major applications, including social choice, auctions, matching and mechanism design; and the relevant mathematics of linear programming and fixed point theory. The comprehensive coverage combined with the depth and clarity of exposition makes it an ideal book not only to learn game theory from, but also to have on the shelves of working game theorists.' Ehud Kalai, Kellogg School of Management, Northwestern University
'The best and the most comprehensive textbook for advanced courses in Game Theory.' David Schmeidler, Ohio State University and Tel Aviv University
'There are quite a few good textbooks on game theory now, but for rigor and breadth this one stands out.' Eric S. Maskin, Nobel Laureate in Economics, Harvard University
'This textbook provides an exceptionally clear and comprehensive introduction to both cooperative and noncooperative game theory. It deftly combines a rigorous exposition of the key mathematical results with a wealth of illuminating examples drawn from a wide range of subjects. It is a tour de force.' Peyton Young, University of Oxford
'This is a wonderful introduction to game theory, written in a way that allows it to serve both as a text for a course and as a reference. While the treatment is mathematical, the mathematics is presented in quite an accessible way ... Each chapter concludes with a large set of exercises, which should appeal to a wide range of students. The book is written by leading figures in the field (unfortunately, one of the authors, Michael Maschler, passed away before the completion of the book); their broad view of the field suffuses the material.' Joe Halpern, Cornell University
About the Author
Michael Maschler was a Professor at the Einstein Institute of Mathematics and the Center for the Study of Rationality at the Hebrew University of Jerusalem, Israel. He greatly contributed to cooperative game theory and to repeated games with incomplete information.
Eilon Solan is a Professor in the School of Mathematical Sciences at Tel Aviv University, Israel. The main topic of his research is repeated games. He serves on the editorial board of several academic journals.
Shmuel Zamir is a Professor Emeritus in the Department of Statistics and the Center for the Study of Rationality at the Hebrew University of Jerusalem, Israel. The main topics of his research are games with incomplete information and auction theory. He is the editor-in-chief of the International Journal of Game Theory.
Most helpful customer reviews
24 of 26 people found the following review helpful.
Math, Science and Applied Gaming-- Best of Breed
By Let's Compare Options Preptorial
This text, over 7 years in the making (the main author sadly passed away before completion), is a 1,000 page definitive guide to game theory-- from an applied mathematical perspective. The audience is claimed to be undergrads, grads and researchers, but the math tends to the graduate level unless you've taken and done well in group theory, linear programming and linear algebra, for example, in undergrad, or via self study. There ARE numerous exercises, some undergrad level (most MBA type in applied), but the wonderful exercises pale in comparison to the more formal proofs and research value of this text.
The bib, citations and notes are a cornucopia of VERY CURRENT research in countless fields, and when the publisher's hype calls this a reference work for researchers, it is right!
Game theory used to be almost a stepchild of probability and statistics, because even deterministic games were handled stochastically (games without dice, like chess) for a long time, due to complexity and covariates. Then, zero sum concepts, cooperation vs. competition, derivative trading, dynamical systems such as the rabbit vs. coyote models, etc. gradually made mathematicians begin to think that game theory might be an important and even broader field of math.
Until Ruse and Conway! Those two geniuses, ala the Matrix, Tron, The 13th floor, Avatar, etc. began to posit (especially Conway) that math ITSELF is a SUBSET of game theory, and at its extreme, the essence of an actual unifying field theory. Conway explained this in terms that non math pros can understand-- this fine text takes those ideas (in the sense of the almost limitless applications of game theory) to a much more advanced level of math. If you read Conway (try: On Numbers and Games) you'll see right away how coordinate systems, axioms, integers, etc. can all be rule and positional elements of gaming in Conway's world-- eg. the first rule of any game is to learn the rules. The "board" can then be seen as the axioms, including in math as well as complexity theories and computing.
Many community colleges are creating courses on gaming-- some video game oriented, some more general and math oriented so students can go on in many other related fields, including even Python programming for AI. This text can supplement and generalize that approach, but is really more appropriate for a targeted game theory/math course (or a series of up to 4 courses as outlined by the authors in the intro). Since it is the first of its kind that is up to date and very complete, I'm guessing that it will change curriculum design as well as create new courses.
For example, students on an engineering, economics, math, computer science, and many other tracks could easily take this as an elective OR as a main track with a number of courses, supplemented by more advanced group theory, analysis, linear algebra, differential equations, etc. Everything from search engines to cryptography are employing techniques from this field, including quantum computing. In my opinion linear algebra is a must, as matrices, especially due to many new numeric computing methods, are growing exponentially in use in these fields. If you're new to this field, don't confuse linear algebra (which isn't necessarily linear OR algebra) with linear programming-- finding corner solutions using inequalities, etc. There are NUMEROUS mappings in GT as well as vector payoffs, and Nash theory itself requires significant linear algebra, so don't try this without it! Some topology also is included, but at advanced undergrad, not math major levels.
Even a field as "light" on the surface as game programming involves, a step deeper, inverse kinematics, physics, cellular automata, beziers, tesselation, projective geometry, quaternions, and much more. The growing breadth and depth of sims themselves (including modeling) reflects Conway's insights about the "Game of Life" (in general as well as in CA) and the ubiquitous applications of game theory. As he states, it is as diverse as math itself if you're willing to consider math one of its subsets!
Highly recommended. The writing is journal quality but not obtuse or show off. The proofs are too brief in some sections, as the authors literally cover the ENTIRE field, but they see this and give ample sources from which to glean more detail. This should be on the shelf of every mathematician as well as those dozens of applied fields to which GT is now being applied, from stock trading to econ, biology, chemistry, physics, ecology and of course human psych!
A less obvious audience might be good math readers who have tired of the 20,000 books on why we make the choices we make, and are ready for the real meat behind decision theory and utility functions, both competitive and cooperative. More than those popular sci titles, this fine volume gives an "aha" mathematically about the hundreds of games we see in front of our eyes daily, but don't necessarily recognize them as such.
This field has advanced by leaps in the last 5 years alone, and it is really great to have a timely and thorough update right now on the whole discipline. There ARE great texts today on each of the aspects, but not nearly as extensive or current. The text is not cheap, but you could spend three times this much adding up the topics with other separate texts, and still not be as current or complete. Other texts (in similar fields) over 1,000 pages are going for over $180 and more when very current, and although I certainly understand budgets, this one is worth it for the amount of work that went into it.
ONE IMPORTANT MISS: This book has nada/nothing/zero on Go! In fact, there really is very little info on non-chance combinatorial games in general, except a small section on zero sum games that also doesn't mention go. In that section the authors state that "no cooperative effort is possible in this category of games." From a utility function view, they are right since there has to be a winner and a loser, but there is a TON of cooperation possible in go-- including the choice of whether to carve out non competitive territory, or go at it tooth and nail! It's not surprising that Western mathematicians don't spend a lot of time on go, even though it is perhaps the most mathematically complex game known, and most single digit kyus like myself can beat the best computer programs available, unlike in chess. In fact, a large Western international chess meeting might have over 5,000 attendees, and you're lucky to get 400 for go in the West!
The authors state that they only cover combinatorials (zero sums) for historical reference, as their math is now so relatively simple. Not so with go! With 31 million seconds in a year and trillions of teraflops of processing per second, it would still take over 10^200 years to brute force the moves-- much longer than the current 1,000 trillion years left until the estimated end of the known universe! Tablebases for endings are similarly weak compared to chess. There isn't even a listing for "go" or "combinatorial games" in the index. Need to fill this gap? I recommend: Nowakowski (Games of No Chance (Mathematical Sciences Research Institute Publications) and Albert (Lessons in Play: An Introduction to Combinatorial Game Theory) both available resonably used from time to time.
FORMAT NOTE: Game theory books are generally written by computer scientists, economists and/or mathematicians. This text is by three mathematicians, so the rigor and math are extensive (a very good thing). That means that some of the formulas are slaughtered on e-readers. The problem with this for teachers is that the index here is very weak. Since this is from Cambridge but translated from Hebrew, there is no web support for indexing (although we are working with Cambridge to post a free e-index on their site right now for teachers, from their Adobe version). For example there is a whole chapter on Chess, and extensive examples that could at least apply to Go from a zero sum perspective, but no index mention of either-- and scanning 1,000 pages visually is, well, tough! Cambridge emailed us that they would send a free e-copy to any teacher ordering the text, but you have to deal with many layers in the UK to make this happen! We'll keep you posted.
Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.
1 of 1 people found the following review helpful.
A feast for those interested in the field.
By D.C. Wolf
This 1000+ page tome on Game Theory is a comprehensive look at game theory that will probably become one of the must-have student textbooks or references. But, if you set aside the mathematics described in detail, theorems and formulas for all of the game theories, there are also very good and varied analogies that are applicable to everyday life and across a broad set of disciplines. More is added as food for thought (if not a student, Mathematician, or scholar), within the pages and in the coursework Exercises.
The theorems and mathematical descriptions begin simply and then build upon each other. Theorems are analyzed and weighed as to their value, but also where they may fall short or are weaker than others in comparison.
There is a handy mathematical Notations description list to reference, and an Appendix with some proofs of theorems and other brief refreshers for those away from math or the field for some time.
As it is written in textbook format, the solutions to the Exercises are not available within these pages.
Not a mathematician, I cannot vouch for the accuracy of the theorems or equations.
A feast for those interested in the field.
(It's a shame Mr. Maschler passed away before realizing and celebrating the completion of this massive work.)
1 of 1 people found the following review helpful.
Must have for advanced students
By Jyotirmoy Bhattacharya
This book will very likely supersede Osborne & Rubinstein [O&R] as the leading graduate text on game theory that emphasizes conceptual and mathematical foundations rather than applications. Unlike the extremely terse O&R, Maschler, Solan and Zamir give many examples and detailed explanations. Full mathematical proofs are given for results like Kuhn's theorem for extensive games or the existence and properties of the universal belief space for games of incomplete information; results which are often only sketched in other texts.
The only weak point of this book is the lack of challenging exercises. There are exercises but they mostly require routine calculation or verification.
Also, the book covers what one might call "classical" game theory. Topics like evolution or learning are not covered. But given that the book is already almost 1,000 pages long one cannot blame the authors for drawing the line somewhere.
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