IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-11-00388.html
   My bibliography  Save this article

Convex Approximation of Bounded Rational Equilibria

Author

Listed:
  • Yusuke Miyazaki

    (SUR Co., Ltd)

  • Hiromi Azuma

    (Accenture Japan Ltd)

Abstract

In this paper, we consider the existence of a sequence of convex sets that has an approximation property for the equilibrium sets in the bounded rational environments. We show that the bounded rational equilibrium multivalued map is approximated with arbitrary precision in the abstract framework, a parameterized class of "general games" together with an associated abstract rationality function that is established by Anderlini and Canning (2001). As an application, we show that the existence of a selection for some bounded rational equilibria on a discontinuous region P when P is a perfect set.

Suggested Citation

  • Yusuke Miyazaki & Hiromi Azuma, 2011. "Convex Approximation of Bounded Rational Equilibria," Economics Bulletin, AccessEcon, vol. 31(4), pages 2869-2874.
    • Handle: RePEc:ebl:ecbull:eb-11-00388
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2011/Volume31/EB-11-V31-I4-P258.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anderlini, Luca & Canning, David, 2001. "Structural Stability Implies Robustness to Bounded Rationality," Journal of Economic Theory, Elsevier, vol. 101(2), pages 395-422, December.
    2. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    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. Miyazaki, Yusuke & Azuma, Hiromi, 2013. "(λ,ϵ)-stable model and essential equilibria," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 85-91.

    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. Miyazaki, Yusuke & Azuma, Hiromi, 2013. "(λ,ϵ)-stable model and essential equilibria," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 85-91.
    2. Yu, Jian & Yang, Zhe & Wang, Neng-Fa, 2016. "Further results on structural stability and robustness to bounded rationality," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 49-53.
    3. Oriol Carbonell-Nicolau & Richard McLean, 2013. "Approximation results for discontinuous games with an application to equilibrium refinement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 1-26, September.
    4. Carbonell-Nicolau, Oriol, 2014. "On essential, (strictly) perfect equilibria," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 157-162.
    5. Messaoud Deghdak & Monique Florenzano, 2011. "On The Existence Of Berge'S Strong Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 325-340.
    6. Carbonell-Nicolau, Oriol & Wohl, Nathan, 2018. "Essential equilibrium in normal-form games with perturbed actions and payoffs," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 108-115.
    7. Fei Xu & Honglei Wang, 2018. "Competitive–Cooperative Strategy Based on Altruistic Behavior for Dual-Channel Supply Chains," Sustainability, MDPI, vol. 10(6), pages 1-15, June.
    8. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    9. Neumann, Berenice Anne, 2022. "Essential stationary equilibria of mean field games with finite state and action space," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 85-91.
    10. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    11. Yu Zhang & Shih-Sen Chang & Tao Chen, 2021. "Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    12. Cea-Echenique, Sebastián & Fuentes, Matías, 2024. "On the continuity of the Walras correspondence in distributional economies with an infinite-dimensional commodity space," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 61-69.
    13. Noguchi, Mitsunori, 2021. "Essential stability of the alpha cores of finite games with incomplete information," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 34-43.
    14. Carbonell-Nicolau, Oriol, 2011. "On strategic stability in discontinuous games," Economics Letters, Elsevier, vol. 113(2), pages 120-123.
    15. Jian-ping Tian & Wen-sheng Jia & Li Zhou, 2024. "Existence and Stability of Fuzzy Slightly Altruistic Equilibrium for a Class of Generalized Multiobjective Fuzzy Games," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 111-125, October.
    16. Sofía Correa & Juan Torres-Martínez, 2014. "Essential equilibria of large generalized games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 479-513, November.
    17. Giuseppe De Marco & Maria Romaniello & Alba Roviello, 2024. "On Hurwicz Preferences in Psychological Games," Games, MDPI, vol. 15(4), pages 1-26, July.
    18. Loi, Andrea & Matta, Stefano, 2015. "Increasing complexity in structurally stable models: An application to a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 20-24.
    19. Zachary Feinstein, 2022. "Continuity and sensitivity analysis of parameterized Nash games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 233-249, October.
    20. Oriol Carbonell-Nicolau, 2015. "Further results on essential Nash equilibria in normal-form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 277-300, June.

    More about this item

    Keywords

    Convex Approximation; Bounded Rational Equilibria; Selection;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    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:ebl:ecbull:eb-11-00388. 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: John P. Conley (email available below). General contact details of provider: .

    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.