Skip to content

Your Cart


You have 0 items in your cart.

Register Sign in Wishlist
Fixed Point Theorems with Applications to Economics and Game Theory

Fixed Point Theorems with Applications to Economics and Game Theory

$67.99 (P)

  • Date Published: July 1989
  • availability: Available
  • format: Paperback
  • isbn: 9780521388085

$ 67.99 (P)

Add to cart Add to wishlist

Other available formats:

Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

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

    Reviews & endorsements

    "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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: July 1989
    • format: Paperback
    • isbn: 9780521388085
    • length: 140 pages
    • dimensions: 225 x 152 x 9 mm
    • weight: 0.22kg
    • availability: Available
  • Table of Contents

    1. Introduction: models and mathematics
    2. Convexity
    3. Simplexes
    4. Sperner's lemma
    5. The Knaster-Kuratowski-Mazurkiewicz lemma
    6. Brouwer's fixed point theorem
    7. Maximization of binary relations
    8. Variational inequalities, price equilibrium, and complementarity
    9. Some interconnections
    10. What good is a completely labelled subsimplex?
    11. Continuity of correspondences
    12. The maximum theorem
    13. Approximation of correspondence
    14. Selection theorems for correspondences
    15. Fixed point theorems for correspondences
    16. Sets with convex sections and a minimax theorem
    17. The Fan-Browder theorem
    18. Equilibrium of excess demand correspondences
    19. Nash equilibrium of games and abstract economies
    20. Walrasian equilibrium of an economy
    21. More interconnections
    22. The Knaster-Kuratowski-Mazurkiewicz-Shapley lemma
    23. Cooperative equilibria of games

  • Author

    Kim C. Border, California Institute of Technology

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.