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Fixed-point-like theorems on subspaces

Author

Listed:
  • 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)).

Suggested Citation

  • Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Cahiers de la Maison des Sciences Economiques b04064, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:mse:wpsorb:b04064
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04064.pdf
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    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    2. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 227-252, October.
    3. repec:hal:journl:halshs-00426441 is not listed on IDEAS
    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. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    6. repec:hal:journl:halshs-00426399 is not listed on IDEAS

    More about this item

    Keywords

    Fixed-point; Grassmannian manifold; degree theory;

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