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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.

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File URL: http://eprints.soton.ac.uk/51816/3/new_unawareness.pdf
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Bibliographic Info

Paper provided by Economics Division, School of Social Sciences, University of Southampton in its series Discussion Paper Series In Economics And Econometrics with number 51816.

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Date of creation: 01 Jan 2007
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Handle: RePEc:stn:sotoec:51816

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References

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  1. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, Elsevier, vol. 76(2), pages 242-271, October.
  2. 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, Springer, vol. 41(2), pages 325-329, May.
  3. Galanis, Spyros, 2013. "Trade and the value of information under unawareness," Discussion Paper Series In Economics And Econometrics, Economics Division, School of Social Sciences, University of Southampton 1313, Economics Division, School of Social Sciences, University of Southampton.
  4. Salvatore Modica & J.-Marc Tallon & Aldo Rustichini, 1998. "Unawareness and bankruptcy: A general equilibrium model," Economic Theory, Springer, Springer, vol. 12(2), pages 259-292.
  5. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, Econometric Society, vol. 47(3), pages 565-77, May.
  6. HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004. "Interactive unawareness," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Aviad Heifetz & Martin Meier & Burkhard Schipper, 2011. "Unawareness, Beliefs, and Speculative Trade," Working Papers, University of California, Davis, Department of Economics 118, University of California, Davis, Department of Economics.
  8. Meier, Martin & Schipper, Burkhard C, 2010. "Speculative Trade under Unawareness: The Infinite Case," MPRA Paper 20632, University Library of Munich, Germany.
  9. Oliver Board, 2006. "Object-Based Unawareness," Working Papers, University of Pittsburgh, Department of Economics 245, University of Pittsburgh, Department of Economics, revised Jan 2006.
  10. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, Elsevier, vol. 28(1), pages 192-200, October.
  11. Aviad Heifetz & Martin Meier & Burkhard Schipper, 2011. "Dynamic unawareness and rationalizable behavior," Working Papers, University of California, Davis, Department of Economics 113, University of California, Davis, Department of Economics.
  12. Paolo Ghirardato, 2001. "Coping with ignorance: unforeseen contingencies and non-additive uncertainty," Economic Theory, Springer, Springer, vol. 17(2), pages 247-276.
  13. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(3), pages 977-993, May.
  14. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 6(4), pages 53-82, Fall.
  15. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 27(2), pages 265-298, May.
  16. Joseph Y. Halpern, 2000. "Alternative Semantics for Unawareness," Game Theory and Information, EconWPA 0004010, EconWPA.
  17. Sujoy Mukerji, 1996. "Understanding the nonadditive probability decision model (*)," Economic Theory, Springer, Springer, vol. 9(1), pages 23-46.
  18. Epstein, Larry G. & Marinacci, Massimo & Seo, Kyoungwon, 2007. "Coarse contingencies and ambiguity," Theoretical Economics, Econometric Society, Econometric Society, vol. 2(4), December.
  19. Ewerhart, Christian, 2001. "Heterogeneous Awareness and the Possibility of Agreement," Sonderforschungsbereich 504 Publications, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim 01-30, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  20. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 639, Cowles Foundation for Research in Economics, Yale University.
  21. Jacob Sagi, 2006. "What is an ‘endogenous state space’?," Economic Theory, Springer, Springer, vol. 27(2), pages 305-320, January.
  22. Aldo Rustichini, 2002. "Preference for flexibility in infinite horizon problems," Economic Theory, Springer, Springer, vol. 20(4), pages 677-702.
  23. 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, The MIT Press, edition 1, volume 1, number 0262541599, December.
  24. Eddie Dekel, 1997. "A Unique Subjective State Space for Unforeseen Contingencies," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1202, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  25. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, Springer, vol. 71(4), pages 593-614, October.
  26. repec:ecl:ucdeco:09-20 is not listed on IDEAS
  27. Youichiro Higashi & Kazuya Hyogo, 2012. "Lexicographic expected utility with a subjective state space," Economic Theory, Springer, Springer, vol. 49(1), pages 175-192, January.
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Citations

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Cited by:
  1. Burkhard Schipper, 2010. "Revealed Unawareness," Working Papers, University of California, Davis, Department of Economics 105, University of California, Davis, Department of Economics.
  2. Aviad Heifetz & Martin Meier & Burkhard Schipper, 2011. "Unawareness, Beliefs, and Speculative Trade," Working Papers, University of California, Davis, Department of Economics 118, University of California, Davis, Department of Economics.
  3. Aviad Heifetz & Martin Meier & Burkhard C. Schipper, 2005. "A Canonical Model for Interactive Unawareness," Bonn Econ Discussion Papers, University of Bonn, Germany bgse23_2005, University of Bonn, Germany.
  4. 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, Springer, vol. 41(2), pages 325-329, May.
  5. Galanis, Spyros, 2013. "Trade and the value of information under unawareness," Discussion Paper Series In Economics And Econometrics, Economics Division, School of Social Sciences, University of Southampton 1313, Economics Division, School of Social Sciences, University of Southampton.
  6. Sarah Auster, 2012. "Asymmetric Awareness and Moral Hazard," Economics Working Papers, European University Institute ECO2012/23, European University Institute.
  7. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, Springer, vol. 71(4), pages 593-614, October.
  8. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer, Springer, vol. 42(3), pages 725-753, August.
  9. Auster, Sarah, 2013. "Asymmetric awareness and moral hazard," Games and Economic Behavior, Elsevier, Elsevier, vol. 82(C), pages 503-521.
  10. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
  11. Ying-Ju Chen & Xiaojian Zhao, 2013. "Solution Concepts of Principal-Agent Models with Unawareness of Actions," Games, MDPI, Open Access Journal, MDPI, Open Access Journal, vol. 4(3), pages 508-531, August.

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