IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2305.08940.html
   My bibliography  Save this paper

Complete Conditional Type Structures

Author

Listed:
  • Nicodemo De Vito

Abstract

Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are modelled by type structures, which allow the analyst to represent the players' hierarchies without specifying an infinite sequence of conditional beliefs. Here, we study type structures that satisfy a "richness" property, called completeness. This property is defined on the type structure alone, without explicit reference to hierarchies of beliefs or other type structures. We provide sufficient conditions under which a complete type structure represents all hierarchies of conditional beliefs. In particular, we present an extension of the main result in Friedenberg (2010) to type structures with conditional beliefs. KEYWORDS: Conditional probability systems, hierarchies of beliefs, type structures, completeness, terminality. JEL: C72, D80

Suggested Citation

  • Nicodemo De Vito, 2023. "Complete Conditional Type Structures," Papers 2305.08940, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2305.08940
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2305.08940
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    2. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    3. Dufwenberg, Martin & Patel, Amrish, 2019. "Introduction to special issue on psychological game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 181-184.
    4. Pierpaolo Battigalli, 2006. "Rationalization In Signaling Games: Theory And Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 67-93.
    5. Pierpaolo Battigalli & Alfredo Di Tillio & Dov Samet, 2011. "Strategies and interactive beliefs in dynamic games," Working Papers 375, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    7. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
    8. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    9. Vittorio Pelligra, 2011. "Intentions, Trust and Frames: A Note on Sociality and the Theory of Games," Review of Social Economy, Taylor & Francis Journals, vol. 69(2), pages 163-188.
    10. Battigalli, Pierpaolo & Dufwenberg, Martin & Smith, Alec, 2019. "Frustration, aggression, and anger in leader-follower games," Games and Economic Behavior, Elsevier, vol. 117(C), pages 15-39.
    11. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    12. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    13. Tsakas, E., 2011. "Hierarchies of conditional beliefs derived from commonly known priors," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    15. Paulo Barelli, 2010. "Consistent Beliefs in Extensive Form Games," Games, MDPI, vol. 1(4), pages 1-7, October.
    16. Pierpaolo Battigalli & Martin Dufwenberg, 2019. "Psychological Game Theory," Working Papers 646, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Cyril Hédoin, 2016. "Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals," Games, MDPI, vol. 7(4), pages 1-17, November.
    18. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics.
    19. Kirchsteiger, Georg & Aldashev, Gani & Sebald, Alexander, 2009. "Decision-making Procedures: A General Theory and Its Field Experimental Test," CEPR Discussion Papers 7365, C.E.P.R. Discussion Papers.
    20. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.

    More about this item

    Keywords

    conditional probability systems; hierarchies of beliefs; type structures; completeness; terminality. jel: c72; d80;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

    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:2305.08940. 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.