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Unawareness of theorems

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  • Spyros Galanis

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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 (J Econ Theory 144:977–993, 2009 ), Heifetz et al. (J Econ Theory 130:78–94, 25 2006 ) 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 (Ann Stat 4:1236–1239, 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. Copyright Springer-Verlag 2013

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 52 (2013)
Issue (Month): 1 (January)
Pages: 41-73

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Handle: RePEc:spr:joecth:v:52:y:2013:i:1:p:41-73

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Related research

Keywords: Unawareness; Uncertainty; Knowledge; Interactive epistemology; Bounded perception; C70; C72; D80; D82;

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References

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  1. Eddie Dekel, 1997. "A Unique Subjective State Space for Unforeseen Contingencies," Discussion Papers 1202, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Ghirardato, Paolo, 1996. "Coping With Ignorance: Unforeseen Contingencies and Non-Additive Uncertainty," Working Papers 945, California Institute of Technology, Division of the Humanities and Social Sciences.
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  8. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2005. "Interactive Unawareness," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 52, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  9. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
  10. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
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  13. Ewerhart, Christian, 2001. "Heterogeneous Awareness and the Possibility of Agreement," Sonderforschungsbereich 504 Publications 01-30, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  14. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2009. "Unawareness, Beliefs and Speculative Trade," MPRA Paper 18437, University Library of Munich, Germany.
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  17. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  18. Meier, Martin & Schipper, Burkhard C, 2010. "Speculative Trade under Unawareness: The Infinite Case," MPRA Paper 20632, University Library of Munich, Germany.
  19. 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, vol. 41(2), pages 325-329, May.
  20. Sujoy Mukerji, 1996. "Understanding the nonadditive probability decision model (*)," Economic Theory, Springer, vol. 9(1), pages 23-46.
  21. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
  22. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
  23. Salvatore Modica & J.-Marc Tallon & Aldo Rustichini, 1998. "Unawareness and bankruptcy: A general equilibrium model," Economic Theory, Springer, vol. 12(2), pages 259-292.
  24. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  25. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
  26. 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.
  27. Jacob Sagi, 2006. "What is an ‘endogenous state space’?," Economic Theory, Springer, vol. 27(2), pages 305-320, January.
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Citations

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Cited by:
  1. 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 508-531, August.
  2. Aviad Heifetz & Martin Meier & Burkhard C. Schipper, 2005. "A Canonical Model for Interactive Unawareness," Bonn Econ Discussion Papers bgse23_2005, University of Bonn, Germany.
  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. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer, vol. 42(3), pages 725-753, August.
  5. Burkhard Schipper, 2010. "Revealed Unawareness," Working Papers 105, University of California, Davis, Department of Economics.
  6. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
  7. 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.
  8. Auster, Sarah, 2013. "Asymmetric awareness and moral hazard," Games and Economic Behavior, Elsevier, vol. 82(C), pages 503-521.
  9. Sarah Auster, 2012. "Asymmetric Awareness and Moral Hazard," Economics Working Papers ECO2012/23, European University Institute.
  10. 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, vol. 41(2), pages 325-329, May.
  11. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.

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