IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v46y2017i2d10.1007_s00182-016-0534-x.html
   My bibliography  Save this article

Characterizations of perfect recall

Author

Listed:
  • Carlos Alós-Ferrer

    (University of Cologne)

  • Klaus Ritzberger

    (Institute for Advanced Studies, Vienna, and Vienna Graduate School of Finance)

Abstract

This paper considers the condition of perfect recall for the class of arbitrarily large discrete extensive form games. The known definitions of perfect recall are shown to be equivalent even beyond finite games. Further, a qualitatively new characterization in terms of choices is obtained. In particular, an extensive form game satisfies perfect recall if and only if the set of choices, viewed as sets of ultimate outcomes, fulfill the “Trivial Intersection” property, that is, any two choices with nonempty intersection are ordered by set inclusion.

Suggested Citation

  • Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizations of perfect recall," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 311-326, May.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0534-x
    DOI: 10.1007/s00182-016-0534-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-016-0534-x
    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/s00182-016-0534-x?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. Carlos Alós-Ferrer & Klaus Ritzberger, 2013. "Large extensive form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 75-102, January.
    2. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
    3. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    4. Carlos Alós-Ferrer & Klaus Ritzberger, 2005. "Trees and decisions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 763-798, June.
    5. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    6. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    7. Wichardt, Philipp C., 2008. "Existence of Nash equilibria in finite extensive form games with imperfect recall: A counterexample," Games and Economic Behavior, Elsevier, vol. 63(1), pages 366-369, May.
    8. Klaus Ritzberger, 1999. "Recall in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 69-87.
    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. Hillas, John & Kvasov, Dmitriy, 2020. "Backward induction in games without perfect recall," Games and Economic Behavior, Elsevier, vol. 124(C), pages 207-218.
    2. Pierpaolo Battigalli & Nicolò Generoso, 2021. "Information Flows and Memory in Games," Working Papers 678, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

    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. Pierpaolo Battigalli & Nicolò Generoso, 2021. "Information Flows and Memory in Games," Working Papers 678, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    3. Peter A. Streufert, 2019. "Equivalences among five game specifications, including a new specification whose nodes are sets of past choices," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 1-32, March.
    4. Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizing existence of equilibrium for large extensive form games: a necessity result," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 407-430, February.
    5. Mackenzie, Andrew, 2020. "A revelation principle for obviously strategy-proof implementation," Games and Economic Behavior, Elsevier, vol. 124(C), pages 512-533.
    6. J. Jude Kline & Shravan Luckraz, 2016. "Equivalence between graph-based and sequence-based extensive form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 85-94, April.
    7. Carlos Alós-Ferrer & Klaus Ritzberger, 2013. "Large extensive form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 75-102, January.
    8. Burkhard Schipper, 2017. "Kuhn's Theorem for Extensive Games with Unawareness," Working Papers 176, University of California, Davis, Department of Economics.
    9. Shravan Luckraz, 2019. "A Survey on the Relationship Between the Game of Cops and Robbers and Other Game Representations," Dynamic Games and Applications, Springer, vol. 9(2), pages 506-520, June.
    10. Lambert, Nicolas S. & Marple, Adrian & Shoham, Yoav, 2019. "On equilibria in games with imperfect recall," Games and Economic Behavior, Elsevier, vol. 113(C), pages 164-185.
    11. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
    12. Peter A. Streufert, 2015. "Choice-Set Forms are Dual to Outcome-Set Forms," University of Western Ontario, Departmental Research Report Series 20153, University of Western Ontario, Department of Economics.
    13. Burkhard Schipper, 2017. "Kuhn's Theorem for Extensive Games with Unawareness," Working Papers 204, University of California, Davis, Department of Economics.
    14. Alós-Ferrer, Carlos & Kern, Johannes, 2015. "Repeated games in continuous time as extensive form games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 34-57.
    15. Streufert, Peter, 2018. "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms," MPRA Paper 90490, University Library of Munich, Germany.
    16. Battigalli, Pierpaolo & Leonetti, Paolo & Maccheroni, Fabio, 2020. "Behavioral equivalence of extensive game structures," Games and Economic Behavior, Elsevier, vol. 121(C), pages 533-547.
    17. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
    18. Carlos Pimienta, 2014. "Bayesian and consistent assessments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 601-617, April.
    19. Uwe Dulleck, 2007. "The E-Mail Game Revisited — Modeling Rough Inductive Reasoning," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 323-339.
    20. Kaneko, Mamoru & Kline, J. Jude, 2008. "Inductive game theory: A basic scenario," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1332-1363, December.

    More about this item

    Keywords

    Perfect recall; Large extensive form games; Non-cooperative games;
    All these keywords.

    JEL classification:

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

    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:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0534-x. 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.