IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2006.14838.html
   My bibliography  Save this paper

Kuhn's Equivalence Theorem for Games in Intrinsic Form

Author

Listed:
  • Benjamin Heymann

    (CERMICS)

  • Michel de Lara

    (CERMICS)

  • Jean-Philippe Chancelier

    (CERMICS)

Abstract

We state and prove Kuhn's equivalence theorem for a new representation of games, the intrinsic form. First, we introduce games in intrinsic form where information is represented by $\sigma$-fields over a product set. For this purpose, we adapt to games the intrinsic representation that Witsenhausen introduced in control theory. Those intrinsic games do not require an explicit description of the play temporality, as opposed to extensive form games on trees. Second, we prove, for this new and more general representation of games, that behavioral and mixed strategies are equivalent under perfect recall (Kuhn's theorem). As the intrinsic form replaces the tree structure with a product structure, the handling of information is easier. This makes the intrinsic form a new valuable tool for the analysis of games with information.

Suggested Citation

  • Benjamin Heymann & Michel de Lara & Jean-Philippe Chancelier, 2020. "Kuhn's Equivalence Theorem for Games in Intrinsic Form," Papers 2006.14838, arXiv.org.
    • Handle: RePEc:arx:papers:2006.14838
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2006.14838
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    2. Carlos Alós-Ferrer & Klaus Ritzberger, 2016. "The Theory of Extensive Form Games," Springer Series in Game Theory, Springer, number 978-3-662-49944-3.
    3. Bonanno, Giacomo, 2004. "Memory and perfect recall in extensive games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 237-256, May.
    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. Battigalli, Pierpaolo & Generoso, Nicolò, 2024. "Information flows and memory in games," Games and Economic Behavior, Elsevier, vol. 145(C), pages 356-376.
    2. Heymann, Benjamin & De Lara, Michel & Chancelier, Jean-Philippe, 2022. "Kuhn's equivalence theorem for games in product form," Games and Economic Behavior, Elsevier, vol. 135(C), pages 220-240.
    3. Emiliano Catonini, 2022. "A Dutch book argument for belief consistency," Papers 2202.10121, arXiv.org.
    4. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    5. Hammond, Peter J., 1999. "Non-Archimedean subjective probabilities in decision theory and games," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 139-156, September.
    6. Asheim, Geir & Søvik, Ylva, 2003. "The semantics of preference-based belief operators," Memorandum 05/2003, Oslo University, Department of Economics.
    7. Peter A. Streufert, 2006. "Products of Several Relative Probabilities," University of Western Ontario, Departmental Research Report Series 20061, University of Western Ontario, Department of Economics.
    8. Giacomo Bonanno, 2009. "A characterization of sequential equilibrium in terms of AGM belief revision," Working Papers 33, University of California, Davis, Department of Economics.
    9. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 11, University of California, Davis, Department of Economics.
    10. Heifetz Aviad & Meier Martin & Schipper Burkhard C., 2021. "Prudent Rationalizability in Generalized Extensive-form Games with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 525-556, June.
    11. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    12. Catonini, Emiliano & De Vito, Nicodemo, 2024. "Cautious belief and iterated admissibility," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    13. Giacomo Bonanno, 2013. "AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 567-592, August.
    14. 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.
    15. Battigalli, Pierpaolo & Leonetti, Paolo & Maccheroni, Fabio, 2020. "Behavioral equivalence of extensive game structures," Games and Economic Behavior, Elsevier, vol. 121(C), pages 533-547.
    16. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    17. Charles F. Manski, 2008. "Partial Prescriptions For Decisions With Partial Knowledge," NBER Working Papers 14396, National Bureau of Economic Research, Inc.
    18. Alicia Vidler & Toby Walsh, 2024. "Non cooperative Liquidity Games and their application to bond market trading," Papers 2405.02865, arXiv.org.
    19. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
    20. János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2006.14838. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.