IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v4y2016i1d10.1007_s40505-016-0094-z.html
   My bibliography  Save this article

Equivalence between graph-based and sequence-based extensive form games

Author

Listed:
  • J. Jude Kline

    (University of Queensland)

  • Shravan Luckraz

    (University of Nottingham)

Abstract

This note establishes an equivalence between the graph-based definition of an infinite extensive form game [following Kuhn (Contributions to the theory of games II, Princeton: Princeton University Press, pp 193–216, 1953)] and the sequence-based definition by Osborne and Rubinstein (A course in game theory, Cambridge: MIT Press, 1994).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:etbull:v:4:y:2016:i:1:d:10.1007_s40505-016-0094-z
    DOI: 10.1007/s40505-016-0094-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-016-0094-z
    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/s40505-016-0094-z?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. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    2. Dubey, Pradeep & Kaneko, Mamoru, 1985. "Information patterns and Nash equilibria in extensive games -- II," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 247-262, December.
    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. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    5. Mamoru Kaneko & J. Kline, 2013. "Partial memories, inductively derived views, and their interactions with behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 27-59, May.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    7. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
    8. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
    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. Subir K. Chakrabarti & Iryna Topolyan, 2016. "An extensive form-based proof of the existence of sequential equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 355-365, October.
    2. 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.
    3. Shravan Luckraz & Bruno Antonio Pansera, 2022. "A Note on the Concept of Time in Extensive Games," Mathematics, MDPI, vol. 10(8), pages 1-4, April.
    4. 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.
    5. Peter A. Streufert, 2020. "The Category of Node-and-Choice Extensive-Form Games," Papers 2004.11196, arXiv.org, revised Jul 2020.
    6. 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. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    2. 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.
    3. 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.
    4. Battigalli, Pierpaolo & Generoso, Nicolò, 2024. "Information flows and memory in games," Games and Economic Behavior, Elsevier, vol. 145(C), pages 356-376.
    5. Kaneko, Mamoru & Kline, J. Jude, 2008. "Inductive game theory: A basic scenario," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1332-1363, December.
    6. 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.
    7. Jamison Julian C., 2014. "Two Examples of Equilibrium Nonexistence," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 55-60, July.
    8. 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.
    9. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
    10. Mackenzie, Andrew, 2020. "A revelation principle for obviously strategy-proof implementation," Games and Economic Behavior, Elsevier, vol. 124(C), pages 512-533.
    11. Wang, Yafeng & Graham, Brett, 2009. "Generalized Maximum Entropy estimation of discrete sequential move games of perfect information," MPRA Paper 21331, University Library of Munich, Germany.
    12. 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.
    13. 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.
    14. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    15. Heller, Yuval & Solan, Eilon & Tomala, Tristan, 2012. "Communication, correlation and cheap-talk in games with public information," Games and Economic Behavior, Elsevier, vol. 74(1), pages 222-234.
    16. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    17. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    18. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2011. "Prudent rationalizability in generalized extensive-form games," MPRA Paper 30220, University Library of Munich, Germany.
    19. 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.
    20. Julio González-Díaz & Miguel Meléndez-Jiménez, 2014. "On the notion of perfect Bayesian equilibrium," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 128-143, April.

    More about this item

    Keywords

    Extensive form games; Equivalence theorems; Graph theory;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    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:etbull:v:4:y:2016:i:1:d:10.1007_s40505-016-0094-z. 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.