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On the relationship between hierarchy and type morphisms

Author

Listed:
  • Amanda Friedenberg

    (W.P. Carey School of Business)

  • Martin Meier

    (Institut für Höhere Studien
    Instituto de Analisis Economico)

Abstract

Here, we establish a relationship between hierarchy and type morphisms. Both concepts have been used to relate the types in one structure to types in a second “larger” structure. In general, the two concepts may differ, in the sense that a hierarchy morphism need not be a type morphism. We provide a necessary and sufficient condition under which the two concepts coincide. We go on to provide situations under which this condition must be satisfied.

Suggested Citation

  • Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
    • Handle: RePEc:spr:joecth:v:46:y:2011:i:3:d:10.1007_s00199-010-0517-2
    DOI: 10.1007/s00199-010-0517-2
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    References listed on IDEAS

    as
    1. Heifetz, Aviad & Samet, Dov, 1999. "Coherent beliefs are not always types," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 475-488, December.
    2. Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
    3. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    4. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    5. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    6. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    7. Pierpaolo Battigalli & Amanda Friedenberg, 2009. "Context-Dependent Forward Induction Reasoning," Working Papers 351, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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    Cited by:

    1. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).

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    More about this item

    Keywords

    Hierarchies of beliefs; Type structures; Epistemic game theory; Morphisms;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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