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Fixed-point-like theorems on subspaces

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Author Info
Philippe Bich () (CEREMADE)
Bernard Cornet () (CERMSEM)

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Abstract

In this paper, we prove a fixed-point-like theorem for multi-valued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems : the fixed-point-like theorem by Hirsh, Magill, Mas-Colell (1990) or Husseiny, Lasry, Magill (1990) and the fixed-point theorem by Gale, Mas-Colell (1975) (which generalizes Kakutani's theorem (1941)).

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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04064.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b04064.

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Length: 14 pages
Date of creation: Jun 2004
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Handle: RePEc:mse:wpsorb:b04064

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Keywords: Fixed-point; Grassmannian manifold; degree theory;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67. [Downloadable!] (restricted)
  2. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June. [Downloadable!] (restricted)
  3. Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Â Zaier Aouani & Â Bernard Cornet, 2009. "Existence of financial equilibria with restricted participation," Working Papers 001-09, International School of Economics at TSU, Tbilisi, Republic of Georgia. [Downloadable!]
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