IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00265464.html
   My bibliography  Save this paper

An answer to a question of herings et al

Author

Listed:
  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of $\R^n$, and not only polytopes. This fixed point theorem can be applied to the problem of Nash equilibrium existence in discontinuous games.

Suggested Citation

  • Philippe Bich, 2008. "An answer to a question of herings et al," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265464, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00265464
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00265464
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00265464/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman & Zaifu Yang, 2004. "A Fixed Point Theorem for Discontinuous Functions," Tinbergen Institute Discussion Papers 05-004/1, Tinbergen Institute.
    2. Candelon, B. & Kool, C.J.M. & Raabe, K. & van Veen, A.P., 2005. "The feasibility of a fixed exchange rate regime for new EU-members: evidence from real exchange rates," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Toussaint, Sabine, 1984. "On the existence of equilibria in economies with infinitely many commodities and without ordered preferences," Journal of Economic Theory, Elsevier, vol. 33(1), pages 98-115, June.
    Full references (including those not matched with items on IDEAS)

    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. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Cahiers de la Maison des Sciences Economiques b06066, Université Panthéon-Sorbonne (Paris 1).
    2. Takao Fujimoto, 2013. "Fixed Point Theorems for Discontinuous Maps on a Non-convex Domain," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 547-572, July.
    3. Philippe Bich, 2008. "An answer to a question of herings et al," Post-Print halshs-00287667, HAL.
    4. Philippe Bich, 2008. "An answer to a question of herings et al," Working Papers halshs-00265464, HAL.
    5. Robert M. Anderson & Haosui Duanmu & M. Ali Khan & Metin Uyanik, 2022. "Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 387-412, April.
    6. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    7. 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.
    8. Noguchi, Mitsunori, 1997. "Economies with a continuum of agents with the commodity-price pairing (l[infin], l1)," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 265-287, October.
    9. Florenzano Monique, 1991. "Quasiequilibria in abstract economies application to the overlapping generations models," CEPREMAP Working Papers (Couverture Orange) 9117, CEPREMAP.
    10. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    11. Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, University Library of Munich, Germany.
    12. Z. Yang & Y. J. Pu, 2011. "Essential Stability of Solutions for Maximal Element Theorem with Applications," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 284-297, August.
    13. Bagh, Adib, 1998. "Equilibrium in abstract economies without the lower semi-continuity of the constraint maps," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 175-185, September.
    14. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    15. Noguchi, Mitsunori, 1997. "Economies with a continuum of consumers, a continuum of suppliers and an infinite dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 1-21, February.
    16. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Post-Print halshs-00119033, HAL.
    17. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    18. C. Ionescu Tulcea, 1987. "On the Approximation of Upper Semi-Continuous Correspondences and the Equilibriums of Generalized Games," Discussion Papers 736, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Zaifu Yang, 2008. "On the Solutions of Discrete Nonlinear Complementarity and Related Problems," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 976-990, November.
    20. Philippe Bich, 2008. "An answer to a question of herings et al," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00287667, HAL.

    More about this item

    Keywords

    fixed point theorem; discontinuity; nash equilibrium;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:hal:cesptp:halshs-00265464. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.