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Probabilistic Unawareness

Author

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  • Mikaël Cozic

    (LIS - Lettres, Idées, Savoirs - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12, IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques - UP1 - Université Paris 1 Panthéon-Sorbonne - DEC - Département d'Etudes Cognitives - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level, and then axiomatized by Heifetz and Mongin (2001). The paper embodies in this framework those properties of unawareness that have been highlighted in the seminal paper by Modica and Rustichini (1999). Their paper deals with full belief, but we argue that the properties in question also apply to partial belief. Our main result is a (soundness and) completeness theorem that reunites the two strands-modal and probabilistic-of doxastic logic.

Suggested Citation

  • Mikaël Cozic, 2016. "Probabilistic Unawareness," Post-Print hal-01950702, HAL.
    • Handle: RePEc:hal:journl:hal-01950702
    DOI: 10.3390/g7040038
    Note: View the original document on HAL open archive server: https://hal.science/hal-01950702
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    References listed on IDEAS

    as
    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    2. Spyros Galanis, 2013. "Unawareness of theorems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 41-73, January.
    3. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    4. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    5. Bernard Walliser, 2008. "Cognitive Economics," Springer Books, Springer, number 978-3-540-71347-0, January.
    6. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    7. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
    8. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
    9. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    10. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    11. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    12. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    13. Leandro Rêgo & Joseph Halpern, 2012. "Generalized solution concepts in games with possibly unaware players," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 131-155, February.
    14. Yi-Chun Chen & Jeffrey Ely & Xiao Luo, 2012. "Note on unawareness: Negative Introspection versus AU Introspection (and KU Introspection)," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 325-329, May.
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    Cited by:

    1. Katarina Kostelić, 2023. "Implications of (un)awareness for decision-making in strategic interaction: another take on the Prisoner’s dilemma," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 50(2), pages 251-268, June.

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    More about this item

    Keywords

    C72; unawareness; epistemic logic; probabilistic logic JEL Classification: C70; D80;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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