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Computing Equilibria and Fixed Points

The Solution of Nonlinear Inequalities

  • Book
  • © 1999

Overview

Authors:
  1. Zaifu Yang

    1. Yokohama National University, Japan

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Part of the book series: Theory and Decision Library C (TDLC, volume 21)

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Table of contents (14 chapters)

  1. Front Matter

    Pages N3-x
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  2. Mathematical Preliminaries

    • Zaifu Yang
    Pages 1-35

  3. Applications in Game Theory and Economics

    • Zaifu Yang
    Pages 37-59

  4. First Algorithms for Approximating Fixed Points on the Unit Simplex

    • Zaifu Yang
    Pages 61-77

  5. Simplicial Homotopy Algorithms

    • Zaifu Yang
    Pages 79-100

  6. Variable Dimension Restart Algorithms

    • Zaifu Yang
    Pages 101-113

  7. An Integer Labeling Algorithm for Solving a Class of Integer Programming Problems

    • Zaifu Yang
    Pages 115-145

  8. Refinement and Stability of Stationary Points

    • Zaifu Yang
    Pages 147-170

  9. The Computation of a Continuum of Zero Points of a Point-to-Set Mapping

    • Zaifu Yang
    Pages 171-194

  10. The Computation of Stationary Points on General Polytopes

    • Zaifu Yang
    Pages 195-216

  11. The Computation of Antipodal Fixed Points

    • Zaifu Yang
    Pages 217-237

  12. Kuhn’s Method for Finding All Roots of Univariate Polynomials

    • Zaifu Yang
    Pages 239-263

  13. Gröbner Bases for Solving Multivariate Polynomial Equations

    • Zaifu Yang
    Pages 265-288

  14. Intersection Theory

    • Zaifu Yang
    Pages 289-309

  15. Sperner Theory

    • Zaifu Yang
    Pages 311-322

  16. Back Matter

    Pages 323-344
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Keywords

About this book

Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationary points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Gröbner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).

Authors and Affiliations

  • Yokohama National University, Japan

    Zaifu Yang

Bibliographic Information

  • Book Title: Computing Equilibria and Fixed Points

  • Book Subtitle: The Solution of Nonlinear Inequalities

  • Authors: Zaifu Yang

  • Series Title: Theory and Decision Library C

  • DOI: https://doi.org/10.1007/978-1-4757-4839-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1999

  • Hardcover ISBN: 978-0-7923-8395-6Published: 30 November 1998

  • Softcover ISBN: 978-1-4419-5070-3Published: 08 December 2010

  • eBook ISBN: 978-1-4757-4839-0Published: 17 April 2013

  • Series ISSN: 0924-6126

  • Series E-ISSN: 2194-3044

  • Edition Number: 1

  • Number of Pages: X, 344

  • Topics: Economic Theory/Quantitative Economics/Mathematical Methods

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