IDEAS home Printed from https://ideas.repec.org/p/uwo/uwowop/20153.html
   My bibliography  Save this paper

Choice-Set Forms are Dual to Outcome-Set Forms

Author

Abstract

Alos-Ferrer and Ritzberger (2013) specify each node in a game tree as the set of outcomes that yet remain conceivable. In contrast, Streufert (2015a) specifies each node as the set of choices that have already been made. The symmetry suggests that the two formulations are "dual" in some sense. In this paper I develop this duality. In particular, I define suitable conversion procedures, and show that there is a one-to-one correspondence between choice-set forms and outcome-set forms. The analysis encompasses discrete forms with finite or infinite horizons.

Suggested Citation

  • 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.
    • Handle: RePEc:uwo:uwowop:20153
    as

    Download full text from publisher

    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1258&context=economicsresrpt
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Peter A. Streufert, 2015. "Specifying Nodes as Sets of Choices," University of Western Ontario, Departmental Research Report Series 20151, University of Western Ontario, Department of Economics.
    3. 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.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, 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. 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.

    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. 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.
    2. 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.
    3. Mackenzie, Andrew, 2020. "A revelation principle for obviously strategy-proof implementation," Games and Economic Behavior, Elsevier, vol. 124(C), pages 512-533.
    4. 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.
    5. Battigalli, Pierpaolo & Leonetti, Paolo & Maccheroni, Fabio, 2020. "Behavioral equivalence of extensive game structures," Games and Economic Behavior, Elsevier, vol. 121(C), pages 533-547.
    6. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    7. Battigalli, Pierpaolo & Generoso, Nicolò, 2024. "Information flows and memory in games," Games and Economic Behavior, Elsevier, vol. 145(C), pages 356-376.
    8. 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.
    9. Kaneko, Mamoru & Kline, J. Jude, 2008. "Inductive game theory: A basic scenario," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1332-1363, December.
    10. 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.
    11. Oliver Board, 2002. "The Deception of the Greeks: Generalizing the Information Structure of Extensive Form Games," Economics Series Working Papers 137, University of Oxford, Department of Economics.
    12. 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.
    13. Peter A. Streufert, 2020. "The Category of Node-and-Choice Extensive-Form Games," University of Western Ontario, Departmental Research Report Series 20204, University of Western Ontario, Department of Economics.
    14. Nicola Dimitri, 2009. "Dynamic consistency in extensive form decision problems," Theory and Decision, Springer, vol. 66(4), pages 345-354, April.
    15. Burkhard Schipper, 2017. "Kuhn's Theorem for Extensive Games with Unawareness," Working Papers 176, University of California, Davis, Department of Economics.
    16. Giacomo Bonanno, 2016. "AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1071-1094, November.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    More about this item

    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:uwo:uwowop:20153. 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: the person in charge (email available below). General contact details of provider: https://economics.uwo.ca/research/research_papers/department_working_papers.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.