IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/818.html
   My bibliography  Save this paper

On Continuity of Robust Equilibria

Author

Listed:
  • Ori Haimanko

    (Department of Economics, Ben-Gurion University)

  • Atsushi Kajii

    (Institute of Economic Research, Kyoto University)

Abstract

We relax the Kajii and Morris (1997a) notion of equilibrium ro- bustness by allowing approximate equilibria when information in a game becomes incomplete. The new notion is termed "approximate robustness". The approximately robust equilibrium correspondence turns out to be upper hemicontinuous, unlike the (exactly) robust equilibrium correspondence. Another distinction comes to light when we show that, as a corollary of upper hemicontinuity, approximately robust equilibria exist in all zero-sum games. Thus, although approx- imate robustness is only a small variation of the original notion, it is strictly weaker than the latter, and its adoption enriches the domain of games for which robust equilibria exist.

Suggested Citation

  • Ori Haimanko & Atsushi Kajii, 2012. "On Continuity of Robust Equilibria," KIER Working Papers 818, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:818
    as

    Download full text from publisher

    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP818.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Oyama, Daisuke & Takahashi, Satoru, 2011. "On the relationship between robustness to incomplete information and noise-independent selection in global games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 683-688.
    2. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
    3. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    4. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, 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. Satoru Takahashi, 2020. "Non-equivalence between all and canonical elaborations," The Japanese Economic Review, Springer, vol. 71(1), pages 43-57, January.
    2. Ori Haimanko & Atsushi Kajii, 2016. "Approximate robustness of equilibrium to incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 839-857, November.
    3. Honda, Jun, 2011. "Noise-independent selection in global games and monotone potential maximizer: A symmetric 3×3 example," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 663-669.
    4. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    5. Stephen Morris & Daisuke Oyama & Satoru Takahashi, 2023. "Strict robustness to incomplete information," The Japanese Economic Review, Springer, vol. 74(3), pages 357-376, July.
    6. repec:upd:utmpwp:006 is not listed on IDEAS
    7. Jun Honda, 2018. "Games with the total bandwagon property meet the Quint–Shubik conjecture," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 893-912, September.
    8. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    9. Takahashi, Satoru & Tercieux, Olivier, 2020. "Robust equilibrium outcomes in sequential games under almost common certainty of payoffs," Journal of Economic Theory, Elsevier, vol. 188(C).
    10. Oyama, Daisuke & Takahashi, Satoru, 2015. "Contagion and uninvadability in local interaction games: The bilingual game and general supermodular games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 100-127.
    11. Zenou, Yves & Leister, Matthew & Zhou, Junjie, 2017. "Coordination on Networks," CEPR Discussion Papers 12392, C.E.P.R. Discussion Papers.
    12. Oyama, Daisuke & Takahashi, Satoru, 2011. "On the relationship between robustness to incomplete information and noise-independent selection in global games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 683-688.
    13. Okada, Daijiro & Tercieux, Olivier, 2012. "Log-linear dynamics and local potential," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1140-1164.
    14. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    15. Harry Pei & Bruno Strulovici, 2025. "Robust Implementation with Costly Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 92(1), pages 476-505.
    16. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.
    17. Stephen Morris & Takashi Ui, 2025. "Incomplete Information Robustness," Papers 2502.19075, arXiv.org, revised Feb 2025.
    18. Basteck, Christian & Daniëls, Tijmen R. & Heinemann, Frank, 2013. "Characterising equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2620-2637.
    19. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
    20. Itai Arieli & Ronen Gradwohl & Rann Smorodinsky, 2023. "Informationally Robust Cheap-Talk," Papers 2302.00281, arXiv.org.
    21. UNO, Hiroshi, 2011. "Nested potentials and robust equilibria," LIDAM Discussion Papers CORE 2011009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    incomplete information; robustness; Bayesian Nash equi- librium; ε-equilibrium; upper hemicontinuity; zero-sum games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:kyo:wpaper:818. 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: Makoto Watanabe (email available below). General contact details of provider: https://edirc.repec.org/data/iekyojp.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.