IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/558.html
   My bibliography  Save this paper

Knight-Walras equilibria

Author

Listed:
  • Beißner, Patrick

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and establish their existence. In general, such equilibria lead to Pareto inefficiency and coincide with Arrow-Debreu equilibria only if the values of net trades are ambiguity-free in the mean. Without aggregate uncertainty, inefficiencies arise generically. We introduce a constrained efficiency concept, uncertainty-neutral efficiency and show that Knight-Walras equilibrium allocations are efficient in this constrained sense. Arrow-Debreu equilibria turn out to be non-robust with respect to the introduction of Knightian uncertainty.

Suggested Citation

  • Beißner, Patrick & Riedel, Frank, 2016. "Knight-Walras equilibria," Center for Mathematical Economics Working Papers 558, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:558
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2903538/2903539
    File Function: First Version, 2016
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Blume, Lawrence E. & Cogley, Timothy & Easley, David A. & Sargent, Thomas J. & Tsyrennikov, Viktor, 2018. "A case for incomplete markets," Journal of Economic Theory, Elsevier, vol. 178(C), pages 191-221.
    2. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    3. Dana, Rose-Anne & Riedel, Frank, 2013. "Intertemporal equilibria with Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1582-1605.
    4. Markus K. Brunnermeier & Alp Simsek & Wei Xiong, 2014. "A Welfare Criterion For Models With Distorted Beliefs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1753-1797.
    5. repec:ipg:wpaper:2013-016 is not listed on IDEAS
    6. repec:hal:pseose:hal-00685413 is not listed on IDEAS
    7. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    8. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 1-35, January.
    9. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    10. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    11. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
    12. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    13. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    14. Michael Richter & Ariel Rubinstein, 2015. "Back to Fundamentals: Equilibrium in Abstract Economies," American Economic Review, American Economic Association, vol. 105(8), pages 2570-2594, August.
    15. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    16. Faro, José Heleno, 2015. "Variational Bewley preferences," Journal of Economic Theory, Elsevier, vol. 157(C), pages 699-729.
    17. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    18. repec:ipg:wpaper:16 is not listed on IDEAS
    19. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    20. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    21. repec:dau:papers:123456789/11268 is not listed on IDEAS
    22. 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.
    23. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
    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. Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
    2. Eisei Ohtaki, 2023. "Optimality in an OLG model with nonsmooth preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 611-659, September.
    3. Antoine Billot & Sujoy Mukerji & Jean-Marc Tallon, 2020. "Market Allocations under Ambiguity: A Survey," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 267-282.
    4. Araujo, Aloisio & Chateauneuf, Alain & Faro, José Heleno, 2018. "Financial market structures revealed by pricing rules: Efficient complete markets are prevalent," Journal of Economic Theory, Elsevier, vol. 173(C), pages 257-288.
    5. Strzalecki, Tomasz & Werner, Jan, 2011. "Efficient allocations under ambiguity," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1173-1194, May.
    6. Jeleva, Meglena & Tallon, Jean-Marc, 2016. "Ambiguïté, comportements et marchés financiers," L'Actualité Economique, Société Canadienne de Science Economique, vol. 92(1-2), pages 351-383, Mars-Juin.
    7. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Chateauneuf, Alain & Faro, José Heleno & Tallon, Jean-Marc & Vergopoulos, Vassili, 2024. "Alpha-maxmin as an aggregation of two selves," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    9. Martins-da-Rocha, V. Filipe, 2010. "Interim efficiency with MEU-preferences," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1987-2017, September.
    10. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.
    11. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    12. Madhav Chandrasekher & Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2022. "Dual‐Self Representations of Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(3), pages 1029-1061, May.
    13. König-Kersting, Christian & Kops, Christopher & Trautmann, Stefan T., 2023. "A test of (weak) certainty independence," Journal of Economic Theory, Elsevier, vol. 209(C).
    14. Chambers, Robert G., 2014. "Uncertain equilibria and incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 48-54.
    15. repec:dau:papers:123456789/5375 is not listed on IDEAS
    16. Ghirardato, Paolo & Siniscalchi, Marciano, 2018. "Risk sharing in the small and in the large," Journal of Economic Theory, Elsevier, vol. 175(C), pages 730-765.
    17. Chambers, Christopher P. & Echenique, Federico, 2012. "When does aggregation reduce risk aversion?," Games and Economic Behavior, Elsevier, vol. 76(2), pages 582-595.
    18. Eisei Ohtaki & Hiroyuki Ozaki, 2014. "Optimality in a Stochastic OLG Model with Ambiguity," Working Papers e069, Tokyo Center for Economic Research.
    19. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
    20. Christoph Bühren & Fabian Meier & Marco Pleßner, 2023. "Ambiguity aversion: bibliometric analysis and literature review of the last 60 years," Management Review Quarterly, Springer, vol. 73(2), pages 495-525, June.
    21. Eisei Ohtaki & Hiroyuki Ozaki, 2015. "Monetary equilibria and Knightian uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(3), pages 435-459, August.

    More about this item

    Keywords

    Knightian Uncertainty; Ambiguity; General 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:bie:wpaper:558. 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: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.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.