IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v80y2025i2d10.1007_s00199-024-01588-3.html
   My bibliography  Save this article

Sophisticated reasoning, learning, and equilibrium in repeated games with imperfect feedback

Author

Listed:
  • Pierpaolo Battigalli

    (Bocconi University and IGIER)

  • Davide Bordoli

    (Yale University)

Abstract

We analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated—but impatient—expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning—that is, the ability, in the limit, to exactly forecast the sequence of future observations—thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game.

Suggested Citation

  • Pierpaolo Battigalli & Davide Bordoli, 2025. "Sophisticated reasoning, learning, and equilibrium in repeated games with imperfect feedback," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(2), pages 421-464, September.
    • Handle: RePEc:spr:joecth:v:80:y:2025:i:2:d:10.1007_s00199-024-01588-3
    DOI: 10.1007/s00199-024-01588-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-024-01588-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-024-01588-3?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

    for a different version of it.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:spr:joecth:v:80:y:2025:i:2:d:10.1007_s00199-024-01588-3. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.