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Fixed Point Theorems with Applications to Economics and Game Theory Paperback – July 28, 1989


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Paperback, July 28, 1989
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Product Details

  • Paperback: 140 pages
  • Publisher: Cambridge University Press; Rep Sub edition (July 28, 1989)
  • Language: English
  • ISBN-10: 0521388082
  • ISBN-13: 978-0521388085
  • Product Dimensions: 9.1 x 5.9 x 0.4 inches
  • Shipping Weight: 8.5 ounces (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,350,137 in Books (See Top 100 in Books)

Editorial Reviews

Review

"The book cleanly separates the mathematical theory from the economic applications. Mathematicians, as well as economists, will value this book as a basic, helpful handbook on finite-dimensional fixed-point theorems." Joel Franklin, SIAM Review

"Perhaps the book's greatest strength is that the level of mathematical sophistication it requires is uniform throughout." Timothy J. Kehoe, Journal of Economic Literature

"The organization of the material is novel and interesting and should make the book a useful reference work and perhaps a textbook for a rigorous class on static equilibrium theory of finite competitive economics." Erwin Klein, Mathematical Reviews

Book Description

An introduction to fixed point theory, a body of mathematical techniques for proposing conditions under which sets of assumptions (underlying economic models) have solutions.

Customer Reviews

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Most Helpful Customer Reviews

10 of 11 people found the following review helpful By A Customer on June 2, 2000
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The author compiles theorems, definitions, and properties on a number of topics. There's some convex analysis, maximization of binary relations, fixed point and selection theorems, and various sufficient conditions for existence of equilibria in games and economies.
A nice feature is that the author explains the equivalence or interconnectedness of theorems from different classes -- comparing the KMM lemma to Brouwer's fixed pt. thm., for instance.
This book is extremely useful for its many variations on common principles. Researchers can benefit from consulting it when they have a problem which does not satisfy the usual criteria -- for instance, if you ever have to ask, "I have a correspondence which satisfies all the conditions for Kakutani's theorem except that it is l.h.c. rather than u.h.c.; am I still able to guarantee a fixed point?"
Grad students in micro/game theory can benefit from the survey of theorems, and familiarizing themselves with the many ways they can get to desired results.
The book is compact and thorough with little exposition. Definitions are very clear, and the author is very good at noting when definitions vary, or the same term has multiple definitions in the literature. Though it presents itself as a mathematical text, its audience is clearly economists -- the conditions given and situations described are clearly ones that economists will recognize, and the applications are economic.
A very nice book for people who already know the applications of such theorems and who need minimal explanation.
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7 of 9 people found the following review helpful By A Customer on March 25, 2000
The author, one of the most prominet professors in mathematical economics surveyed fixed point theorems. The theorems are often used to prove the existence of solutions in game theory and economics. If you major in mathematical economics or game theory, you can't avoid to buy this book.
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1 of 1 people found the following review helpful By jacob on July 18, 2013
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This book is an awesome reference for economists or those interested in game theory. It is highly mathematical, so if your mathematical maturity is not very high I would not recommend this book for you. I am finishing up my masters in mathematics and some of it was slow reading even for me. However, if you would be able to read the mathematics I highly recommend it.
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