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Sperner's lemma and competitive equilibrium with incomplete financial markets

Author

Listed:
  • Thanh Le

    (University of Wollongong [Australia])

  • Cuong Le Van

    (CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Ngoc-Sang Pham

    (Métis Lab EM Normandie - EM Normandie - École de Management de Normandie)

  • Cagri Saglam

    (Bilkent University [Ankara])

Abstract

We establish the existence of a competitive equilibrium in a two-period stochastic economy with incomplete financial markets by using Sperner's lemma. Our existence result covers (but is not limited to) several results in the literature, including the cases of nominal and numéraire assets. Moreover, there may exist a continuum of equilibrium prices.

Suggested Citation

  • Thanh Le & Cuong Le Van & Ngoc-Sang Pham & Cagri Saglam, 2024. "Sperner's lemma and competitive equilibrium with incomplete financial markets," Post-Print hal-04552148, HAL.
    • Handle: RePEc:hal:journl:hal-04552148
    DOI: 10.1016/j.econlet.2024.111720
    Note: View the original document on HAL open archive server: https://hal.science/hal-04552148
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    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. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    3. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    4. Thanh Le & Cuong Le Van & Ngoc-Sang Pham & Cagri Saglam, 2022. "A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1072-1080, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Sperner's lemma; fixed-point theorem; general equilibrium; incomplete market; indeterminacy;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • G1 - Financial Economics - - General Financial Markets

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