IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v79y2018icp173-178.html
   My bibliography  Save this article

Local openness: Characterization of a robustness concept for generic sets in function spaces

Author

Listed:
  • Mueller-Frank, Manuel

Abstract

This paper introduces a novel robustness concept for generic sets in function spaces. As motivation, I provide an economically relevant example of a functional property, where a subset of the domain with arbitrary small (Lebesgue) measure marks the difference between the functional property being strongly negligible (nowhere dense) or non-negligible (open). I define a functional property as locally open at some point of the domain if there exists a closed ball around the point such that the functional property is open in the continuous functions on the domain restricted to the ball. A functional property is open if and only if it is locally open everywhere on the domain. Further, a subset of the domain with arbitrary small measure marks the difference between an open and nowhere dense property if and only if the functional property is locally open almost everywhere on the domain.

Suggested Citation

  • Mueller-Frank, Manuel, 2018. "Local openness: Characterization of a robustness concept for generic sets in function spaces," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 173-178.
    • Handle: RePEc:eee:mateco:v:79:y:2018:i:c:p:173-178
    DOI: 10.1016/j.jmateco.2017.10.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406817301192
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2017.10.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, January.
    2. Allen, Beth E, 1981. "Generic Existence of Completely Revealing Equilibria for Economies with Uncertainty when Prices Convey Information," Econometrica, Econometric Society, vol. 49(5), pages 1173-1199, September.
    3. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    4. Yi‐Chun Chen & Siyang Xiong, 2013. "Genericity and Robustness of Full Surplus Extraction," Econometrica, Econometric Society, vol. 81(2), pages 825-847, March.
    5. Philip J Reny & Motty Perry, 2006. "Toward a Strategic Foundation for Rational Expectations Equilibrium," Econometrica, Econometric Society, vol. 74(5), pages 1231-1269, September.
    6. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    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. Gizatulina, Alia & Hellwig, Martin, 2014. "Beliefs, payoffs, information: On the robustness of the BDP property in models with endogenous beliefs," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 136-153.
    2. Fu, Hu & Haghpanah, Nima & Hartline, Jason & Kleinberg, Robert, 2021. "Full surplus extraction from samples," Journal of Economic Theory, Elsevier, vol. 193(C).
    3. Alexander Teytelboym & Shengwu Li & Scott Duke Kominers & Mohammad Akbarpour & Piotr Dworczak, 2021. "Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(3), pages 709-750, July.
    4. Guo, Huiyi, 2024. "Collusion-proof mechanisms for full surplus extraction," Games and Economic Behavior, Elsevier, vol. 145(C), pages 263-284.
    5. Lopomo, Giuseppe & Rigotti, Luca & Shannon, Chris, 2022. "Uncertainty and robustness of surplus extraction," Journal of Economic Theory, Elsevier, vol. 199(C).
    6. Sushil Bikhchandani & Ichiro Obara, 2017. "Mechanism design with information acquisition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 783-812, March.
    7. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    8. Guo, Huiyi, 2019. "Mechanism design with ambiguous transfers: An analysis in finite dimensional naive type spaces," Journal of Economic Theory, Elsevier, vol. 183(C), pages 76-105.
    9. Gizatulina, Alia & Hellwig, Martin, 2017. "The generic possibility of full surplus extraction in models with large type spaces," Journal of Economic Theory, Elsevier, vol. 170(C), pages 385-416.
    10. Farinha Luz, Vitor, 2013. "Surplus extraction with rich type spaces," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2749-2762.
    11. Liu, Bin & Lu, Jingfeng & Wang, Ruqu & Zhang, Jun, 2018. "Optimal prize allocation in contests: The role of negative prizes," Journal of Economic Theory, Elsevier, vol. 175(C), pages 291-317.
    12. Obara Ichiro, 2008. "The Full Surplus Extraction Theorem with Hidden Actions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-28, March.
    13. Qin, Cheng-Zhong & Yang, Chun-Lei, 2009. "An Explicit Approach to Modeling Finite-Order Type Spaces and Applications," University of California at Santa Barbara, Economics Working Paper Series qt8hq7j89k, Department of Economics, UC Santa Barbara.
    14. Zhiwei Liu, 2016. "Implementation of maximin rational expectations equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 813-837, October.
    15. Michael Ostrovsky, 2012. "Information Aggregation in Dynamic Markets With Strategic Traders," Econometrica, Econometric Society, vol. 80(6), pages 2595-2647, November.
    16. Scott Condie & Jayant V. Ganguli, 2011. "Ambiguity and Rational Expectations Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(3), pages 821-845.
    17. Yusuke Kamishiro & Roberto Serrano, 2009. "Equilibrium blocking in large quasilinear economies," Working Papers 2009-12, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    18. Satterthwaite, Mark A. & Williams, Steven R. & Zachariadis, Konstantinos E., 2014. "Optimality versus practicality in market design: A comparison of two double auctions," Games and Economic Behavior, Elsevier, vol. 86(C), pages 248-263.
    19. João Correia-da-Silva & Carlos Hervés-Beloso, 2008. "General equilibrium with private state verification," FEP Working Papers 269, Universidade do Porto, Faculdade de Economia do Porto.
    20. Nicolas S. Lambert & Michael Ostrovsky & Mikhail Panov, 2018. "Strategic Trading in Informationally Complex Environments," Econometrica, Econometric Society, vol. 86(4), pages 1119-1157, July.

    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:eee:mateco:v:79:y:2018:i:c:p:173-178. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.