IDEAS home Printed from https://ideas.repec.org/p/mse/wpsorb/b04064.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04064.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    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. 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.
    4. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    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. Centeno, Alex, 2020. "A Note on the Application of Schubert Calculus in Heterogeneous Economies With Pure Exchange," MPRA Paper 98944, University Library of Munich, Germany.
    4. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Post-Print halshs-00426399, HAL.
    5. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    6. Hichem Ben-El-Mechaiekh & Philippe Bich & Monique Florenzano, 2009. "General equilibrium and fixed-point theory: a partial survey," PSE-Ecole d'économie de Paris (Postprint) hal-00755998, HAL.
    7. Lionel de Boisdeffre, 2021. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information and Restricted Participation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196923, HAL.
    8. Lionel de Boisdeffre, 2021. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information and Restricted Participation," Post-Print halshs-03196923, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Post-Print halshs-03330770, HAL.
    3. Hichem Ben-El-Mechaiekh & Philippe Bich & Monique Florenzano, 2009. "General equilibrium and fixed-point theory: a partial survey," PSE-Ecole d'économie de Paris (Postprint) hal-00755998, HAL.
    4. 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.
    5. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00426399, HAL.
    6. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03330770, HAL.
    7. Bernard Dumas & Andrew Lyasoff, 2012. "Incomplete-Market Equilibria Solved Recursively on an Event Tree," Journal of Finance, American Finance Association, vol. 67(5), pages 1897-1941, October.
    8. Charalambos Aliprantis & Rabee Tourky, 2009. "Equilibria in incomplete assets economies with infinite dimensional spot markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 221-262, February.
    9. Momi, Takeshi, 2001. "Non-existence of equilibrium in an incomplete stock market economy," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 41-70, February.
    10. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    11. Michael Zierhut, 2021. "Indeterminacy of Cournot–Walras equilibrium with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 81-114, February.
    12. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    13. Stahn, Hubert, 1998. "On monopolistic equilibria with incomplete markets: the case of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 83-107, January.
    14. Michele Gori & Marina Pireddu & Antonio Villanacci, 2014. "Existence of financial equilibria with endogenous short selling restrictions and real assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 349-371, October.
    15. Jean-Marc Tallon, 1995. "Théorie de l'équilibre général avec marchés financiers incomplets," Revue Économique, Programme National Persée, vol. 46(5), pages 1207-1239.
    16. Philippe Bich, 2005. "On the existence of approximated equilibria in discontinuous economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00287685, HAL.
    17. Philippe Bich, 2005. "On the existence of approximated equilibria in discontinuous economies," Post-Print halshs-00287685, HAL.
    18. Bottazzi, Jean-Marc, 1995. "Existence of equilibria with incomplete markets: The case of smooth returns," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 59-72.
    19. repec:dau:papers:123456789/6191 is not listed on IDEAS
    20. Polemarchakis, H. M. & Siconolfi, P., 1997. "Generic existence of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 289-311, October.
    21. Pascal Stiefenhofer, 2009. "Production in General Equilibrium with Incomplete Markets," Discussion Papers 09/06, Department of Economics, University of York.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:wpsorb:b04064. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/msep1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.