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Unawareness of theorems

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  • Galanis, Spyros

Abstract

This paper provides a set-theoretic model of knowledge and unawareness. A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent's knowledge, but also, can impair his reasoning about what other agents know. For example, in contrast to Li (2006), Heifetz et al. (2006a) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event. The model follows Aumann (1976) in defining common knowledge and characterizing it in terms of a self-evident event, but departs in showing that no-trade theorems do not hold.

Suggested Citation

  • Galanis, Spyros, 2007. "Unawareness of theorems," Discussion Paper Series In Economics And Econometrics 51816, Economics Division, School of Social Sciences, University of Southampton.
  • Handle: RePEc:stn:sotoec:51816
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    File URL: https://eprints.soton.ac.uk/51816/1/new_unawareness.pdf
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    References listed on IDEAS

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    2. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
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    21. repec:ecl:ucdeco:09-20 is not listed on IDEAS
    22. Galanis, Spyros, 2013. "Trade and the value of information under unawareness," Discussion Paper Series In Economics And Econometrics 1313, Economics Division, School of Social Sciences, University of Southampton.
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    Citations

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    Cited by:

    1. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    2. Burkhard Schipper, 2010. "Revealed Unawareness," Working Papers 105, University of California, Davis, Department of Economics.
    3. Galanis, Spyros, 2016. "The value of information in risk-sharing environments with unawareness," Games and Economic Behavior, Elsevier, vol. 97(C), pages 1-18.
    4. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    5. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    6. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    7. Galanis, Spyros, 2015. "The value of information under unawareness," Journal of Economic Theory, Elsevier, vol. 157(C), pages 384-396.
    8. Konrad Grabiszewski, 2015. "Rationalizing epistemic bounded rationality," Theory and Decision, Springer, vol. 78(4), pages 629-637, April.
    9. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
    10. Auster, Sarah, 2013. "Asymmetric awareness and moral hazard," Games and Economic Behavior, Elsevier, vol. 82(C), pages 503-521.
    11. Mikaël Cozic, 2016. "Probabilistic Unawareness," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-24, November.
    12. Sarah Auster, 2012. "Asymmetric Awareness and Moral Hazard," Economics Working Papers ECO2012/23, European University Institute.
    13. 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.
    14. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2008. "A canonical model for interactive unawareness," Games and Economic Behavior, Elsevier, vol. 62(1), pages 304-324, January.
    15. Ying-Ju Chen & Xiaojian Zhao, 2013. "Solution Concepts of Principal-Agent Models with Unawareness of Actions," Games, MDPI, Open Access Journal, vol. 4(3), pages 1-24, August.
    16. Liu Zhen, 2008. "The Dirty Face Problem with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-20, December.
    17. Simon Grant & J. Kline & Patrick O’Callaghan & John Quiggin, 2015. "Sub-models for interactive unawareness," Theory and Decision, Springer, vol. 79(4), pages 601-613, December.
    18. Galanis, Spyros, 2013. "Trade and the value of information under unawareness," Discussion Paper Series In Economics And Econometrics 1313, Economics Division, School of Social Sciences, University of Southampton.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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