Advertisement

Optima and Equilibria

An Introduction to Nonlinear Analysis

  • Jean-Pierre Aubin

Part of the Graduate Texts in Mathematics book series (GTM, volume 140)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Introduction

    1. Jean-Pierre Aubin
      Pages 1-6
  3. Nonlinear Analysis: Theory

    1. Front Matter
      Pages 7-7
    2. Jean-Pierre Aubin
      Pages 9-19
    3. Jean-Pierre Aubin
      Pages 57-73
    4. Jean-Pierre Aubin
      Pages 101-123
    5. Jean-Pierre Aubin
      Pages 143-166
    6. Jean-Pierre Aubin
      Pages 167-178
    7. Jean-Pierre Aubin
      Pages 179-188
    8. Jean-Pierre Aubin
      Pages 189-209
    9. Jean-Pierre Aubin
      Pages 211-233
  4. Nonlinear Analysis: Exercises and Problems

    1. Front Matter
      Pages 235-235
    2. Jean-Pierre Aubin
      Pages 237-302
    3. Jean-Pierre Aubin
      Pages 303-347
    4. Jean-Pierre Aubin
      Pages 349-400
  5. Back Matter
    Pages 401-437

About this book

Introduction

Advances in game theory and economic theory have proceeded hand in hand with that of nonlinear analysis and in particular, convex analysis. These theories motivated mathematicians to provide mathematical tools to deal with optima and equilibria. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its applications to economics and game theory, has written a rigorous and concise-yet still elementary and self-contained- text-book to present mathematical tools needed to solve problems motivated by economics, management sciences, operations research, cooperative and noncooperative games, fuzzy games, etc. It begins with convex and nonsmooth analysis,the foundations of optimization theory and mathematical programming. Nonlinear analysis is next presented in the context of zero-sum games and then, in the framework of set-valued analysis. These results are applied to the main classes of economic equilibria. The text continues with game theory: noncooperative (Nash) equilibria, Pareto optima, core and finally, fuzzy games. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses. -(See cont. News remarks)

Keywords

Equilibrium Fermat rule Fuzzy games Nash Optimization Theory Pareto Walras analysis convex analysis cooperative and non cooperative games cooperative and non-cooperative games economic models game theory operations research optimization

Authors and affiliations

  • Jean-Pierre Aubin
    • 1
  1. 1.Réseau de Recherche Viabilité, Jeux, ContrôleParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03539-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08446-1
  • Online ISBN 978-3-662-03539-9
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site