IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v68y2010i1p389-402.html
   My bibliography  Save this article

Universality of the Epstein-Wang type structure

Author

Listed:
  • Chen, Yi-Chun

Abstract

We prove that the type structure constructed in [Epstein, L., Wang, T., 1996. 'Belief about belief' without probabilities. Econometrica 64, 1343-1373] is a universal/terminal type structure into which every suitably regular type structure can be embedded. Moreover, it is unique up to a homeomorphism and every belief-complete type space can be mapped onto the universal one. We also show how our results help understand connections among several existing constructions.

Suggested Citation

  • Chen, Yi-Chun, 2010. "Universality of the Epstein-Wang type structure," Games and Economic Behavior, Elsevier, vol. 68(1), pages 389-402, January.
    • Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:389-402
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(09)00096-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    2. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part B : The Central Results," LIDAM Discussion Papers CORE 1994021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    4. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. ,, 2008. "Subjective expected utility in games," Theoretical Economics, Econometric Society, vol. 3(3), September.
    6. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," LIDAM Discussion Papers CORE 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Heifetz, Aviad, 1993. "The Bayesian Formulation of Incomplete Information--The Non-compact Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 329-338.
    8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    9. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    10. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
    11. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    12. Mariotti, Thomas & Meier, Martin & Piccione, Michele, 2005. "Hierarchies of beliefs for compact possibility models," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 303-324, April.
    13. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    14. MERTENS, Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part C : Further Developments," LIDAM Discussion Papers CORE 1994022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Epstein, Larry G. & Peters, Michael, 1999. "A Revelation Principle for Competing Mechanisms," Journal of Economic Theory, Elsevier, vol. 88(1), pages 119-160, September.
    16. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    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. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    2. Galeazzi, Paolo & Marti, Johannes, 2023. "Choice structures in games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 431-455.
    3. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Paolo Galeazzi & Johannes Marti, 2023. "Choice Structures in Games," Papers 2304.11575, arXiv.org.
    5. repec:esx:essedp:722 is not listed 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. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    2. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
    4. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. repec:esx:essedp:722 is not listed on IDEAS
    6. Pintér, Miklós, 2011. "Invariance under type morphisms: the bayesian Nash equilibrium," MPRA Paper 38499, University Library of Munich, Germany.
    7. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    8. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    9. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    10. Meier, Martin, 2008. "Universal knowledge-belief structures," Games and Economic Behavior, Elsevier, vol. 62(1), pages 53-66, January.
    11. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    12. Pintér, Miklós, 2011. "Common priors for generalized type spaces," MPRA Paper 44818, University Library of Munich, Germany.
    13. Salonen, Hannu, 2009. "Common theories," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 279-289, November.
    14. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
    15. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    16. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    17. De Marco, Giuseppe & Romaniello, Maria & Roviello, Alba, 2022. "Psychological Nash equilibria under ambiguity," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 92-106.
    18. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    19. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    20. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    21. Galeazzi, Paolo & Marti, Johannes, 2023. "Choice structures in games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 431-455.

    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:eee:gamebe:v:68:y:2010:i:1:p:389-402. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.