rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Optima and Equilibria
    sub title: an Introduction to Nonlinear Analysis
  name:
    name part: Aubin, Jean Pierre.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 1998
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xvii, 437 pages)
  abstract: 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).
  table of contents: Part I Nonlinear Analysis: Theory: Minimisation Problems: General theorems -- Convex Functions and Proximation, Projection and Separation Theorems -- Conjugate Functions and Convex Minimisation Problems -- Subidfferentials of Convex Functions -- Marginal Properties of Solutions od Convex Minimisation -- Generalised Gradients of Locally Lipschitz Functions -- Two-person Games. Fundamental Concepts and Examples -- Two-person Zero-sum Games: Theorems of Von Neumann and Ky Fan -- Solution of Nonlinear Equations and Inclusions -- Introduction to the Theory of Economic Equilibrium -- The Von Neumann Growth Model -- n-person Games -- Cooperative Games and Fuzzy Games -- Part II Nonlinear Analysis: Examples: Exercises -- Statements of Problems -- Solutions to Problems Appendix: Compendium of Resluts -- References -- Index.
  note: by Jean-Pierre Aubin.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: System theory
  subject:
    topic: Mathematical optimization
  subject:
    topic: Economics
  subject:
    topic: Operations research
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Graduate texts in mathematics ; 140
  identifier: 9783662035399 (electronic bk.)
  identifier: 3662035391 (electronic bk.)
  identifier: 9783642084461
  identifier: 364208446X
  identifier: 3662035391
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130217
    record change date: 20260422160251.8
    record identifier: in00003569709
    language of cataloging:
      language term: eng