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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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File URL: http://hdl.handle.net/10.1007/s00199-011-0683-x
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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. Jacob Sagi, 2006. "What is an ‘endogenous state space’?," Economic Theory, Springer, vol. 27(2), pages 305-320, January.
  2. Salvatore Modica & J.-Marc Tallon & Aldo Rustichini, 1998. "Unawareness and bankruptcy: A general equilibrium model," Economic Theory, Springer, vol. 12(2), pages 259-292.
  3. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
  4. 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.
  5. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  6. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  7. Martin Meier & Burkhard C. Schipper, 2014. "Speculative Trade under Unawareness: The Infinite Case," Working Papers 102, University of California, Davis, Department of Economics.
  8. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
  9. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
  10. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
  11. 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.
  12. Partha Dasgupta & Douglas Gale & Oliver Hart & Eric Maskin (ed.), 1992. "Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262541599, January.
  13. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
  14. Ewerhart, Christian, 2001. "Heterogeneous Awareness and the Possibility of Agreement," Sonderforschungsbereich 504 Publications 01-30, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  15. Aviad Heifetz & Martin Meier & Burkhard Schipper, 2011. "Dynamic unawareness and rationalizable behavior," Working Papers 113, University of California, Davis, Department of Economics.
  16. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
  17. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  18. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  19. repec:ecl:ucdeco:09-20 is not listed on IDEAS
  20. 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.
  21. Mukerji, S., 1995. "Understanding the nonadditive probability decision model," Discussion Paper Series In Economics And Econometrics 9517, Economics Division, School of Social Sciences, University of Southampton.
  22. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  23. Epstein, Larry G. & Marinacci, Massimo & Seo, Kyoungwon, 2007. "Coarse contingencies and ambiguity," Theoretical Economics, Econometric Society, vol. 2(4), December.
  24. Aldo Rustichini, 2002. "Preference for flexibility in infinite horizon problems," Economic Theory, Springer, vol. 20(4), pages 677-702.
  25. Youichiro Higashi & Kazuya Hyogo, 2012. "Lexicographic expected utility with a subjective state space," Economic Theory, Springer, vol. 49(1), pages 175-192, January.
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Citations

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Cited by:
  1. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
  2. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
  3. 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.
  4. Aviad Heifetz & Martin Meier & Burkhard C. Schipper, 2005. "A Canonical Model for Interactive Unawareness," Bonn Econ Discussion Papers bgse23_2005, University of Bonn, Germany.
  5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2009. "Unawareness, Beliefs and Speculative Trade," MPRA Paper 18437, University Library of Munich, Germany.
  6. Schipper, Burkhard C, 2010. "Revealed Unawareness," MPRA Paper 21491, 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. Sarah Auster, 2012. "Asymmetric Awareness and Moral Hazard," Economics Working Papers ECO2012/23, European University Institute.
  9. Auster, Sarah, 2013. "Asymmetric awareness and moral hazard," Games and Economic Behavior, Elsevier, vol. 82(C), pages 503-521.

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