IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v10y2020i1d10.1007_s13235-019-00314-2.html
   My bibliography  Save this article

On Common Belief in Future Rationality in Games with Ambiguous Orderings of Information Sets

Author

Listed:
  • Iryna Topolyan

    (University of Cincinnati)

Abstract

Perea (Games Econ Behav 83:231–254, 2014) introduced common belief in future rationality for dynamic games whose information sets could be unambiguously ordered. It is shown that common belief in future rationality may be possible even in the absence of such an order. We characterize a class of dynamic game forms for which common belief in future rationality is always possible. We introduce a new concept, common belief in future$$^{\star }$$⋆ rationality, which is attained in all dynamic games with perfect recall, regardless of the order of information sets.

Suggested Citation

  • Iryna Topolyan, 2020. "On Common Belief in Future Rationality in Games with Ambiguous Orderings of Information Sets," Dynamic Games and Applications, Springer, vol. 10(1), pages 183-201, March.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:1:d:10.1007_s13235-019-00314-2
    DOI: 10.1007/s13235-019-00314-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-019-00314-2
    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/s13235-019-00314-2?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. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    2. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
    3. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    4. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, November.
    5. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    6. Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
    7. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2002. "Subjective Uncertainty over Behavior Strategies: A Correction," Journal of Economic Theory, Elsevier, vol. 104(2), pages 473-478, June.
    8. Perea, Andres, 2002. "A note on the one-deviation property in extensive form games," Games and Economic Behavior, Elsevier, vol. 40(2), pages 322-338, August.
    9. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, November.
    10. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "The One-Shot-Deviation Principle for Sequential Rationality," Games and Economic Behavior, Elsevier, vol. 12(2), pages 274-282, February.
    11. Klaus Ritzberger, 1999. "Recall in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 69-87.
    12. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    13. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    14. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
    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. Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
    2. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    3. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Rubén Becerril-Borja & Andrés Perea, 2020. "Common belief in future and restricted past rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 711-747, September.
    5. Jagau, Stephan & Perea, Andrés, 2022. "Common belief in rationality in psychological games," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    6. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    7. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    8. Perea, Andrés, 2017. "Forward induction reasoning and correct beliefs," Journal of Economic Theory, Elsevier, vol. 169(C), pages 489-516.
    9. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    10. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    11. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    12. Perea Andrés, 2003. "Rationalizability and Minimal Complexity in Dynamic Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. Perea, Andrés, 2022. "Common belief in rationality in games with unawareness," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 11-30.
    14. Shuige Liu, 2019. "Compactification of Extensive Game Structures and Backward Dominance Procedure," Papers 1905.00355, arXiv.org, revised Nov 2020.
    15. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    16. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 60, University of California, Davis, Department of Economics.
    17. V. K. Oikonomou & J. Jost, 2020. "Periodic Strategies II: Generalizations and Extensions," Papers 2005.12832, arXiv.org.
    18. Andrés Perea & Arkadi Predtetchinski, 2019. "An epistemic approach to stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 181-203, March.
    19. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
    20. Oikonomou, V.K. & Jost, J, 2013. "Periodic strategies and rationalizability in perfect information 2-Player strategic form games," MPRA Paper 48117, University Library of Munich, Germany.

    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:dyngam:v:10:y:2020:i:1:d:10.1007_s13235-019-00314-2. 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: 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.