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Fixed-point-like theorems on subspaces

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  • Philippe Bich

    ()
    (CEREMADE)

  • Bernard Cornet

    ()
    (CERMSEM)

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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Bibliographic Info

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
Date of revision:
Handle: RePEc:mse:wpsorb:b04064

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Related research

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

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References

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  1. 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.
  2. 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.
  3. 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.
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Cited by:
  1. repec:hal:journl:halshs-00426399 is not listed on IDEAS
  2. Zaier Aouani & Bernard Cornet, 2009. "Existence of financial equilibria with restricted participation," Working Papers 001-09, International School of Economics at TSU, Tbilisi, Republic of Georgia.
  3. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
  4. Bernard Cornet & Philippe Bich, 2009. "Existence of pseudo-equilibria in a financial economy," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200910, University of Kansas, Department of Economics, revised Dec 2009.
  5. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer, vol. 45(1), pages 227-252, October.
  6. repec:hal:journl:halshs-00426441 is not listed on IDEAS

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