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Unawareness of theorems

  • Galanis, Spyros

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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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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  1. Youichiro Higashi & Kazuya Hyogo, 2012. "Lexicographic expected utility with a subjective state space," Economic Theory, Springer, vol. 49(1), pages 175-192, January.
  2. Oliver Board, 2006. "Object-Based Unawareness," Working Papers 245, University of Pittsburgh, Department of Economics, revised Jan 2006.
  3. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
  4. Aviad Heifetz & Martin Meier & Burkhard Schipper, 2011. "Dynamic unawareness and rationalizable behavior," Working Papers 113, University of California, Davis, Department of Economics.
  5. Sujoy Mukerji, 1996. "Understanding the nonadditive probability decision model (*)," Economic Theory, Springer, vol. 9(1), pages 23-46.
  6. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  7. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
  8. repec:ecl:ucdeco:09-20 is not listed on IDEAS
  9. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
  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. Martin Meier & Burkhard C. Schipper, 2013. "Speculative Trade under Unawareness: The Infinite Case," Working Papers 102, University of California, Davis, Department of Economics.
  12. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  13. 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.
  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. "Unawareness, Beliefs, and Speculative Trade," Working Papers 118, University of California, Davis, Department of Economics.
  16. Aldo Rustichini, 2002. "Preference for flexibility in infinite horizon problems," Economic Theory, Springer, vol. 20(4), pages 677-702.
  17. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
  18. Salvatore Modica & J.-Marc Tallon & Aldo Rustichini, 1998. "Unawareness and bankruptcy: A general equilibrium model," Economic Theory, Springer, vol. 12(2), pages 259-292.
  19. 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.
  20. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  21. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
  22. 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, June.
  23. HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004. "Interactive unawareness," CORE Discussion Papers 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  24. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  25. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  26. Epstein, Larry G. & Marinacci, Massimo & Seo, Kyoungwon, 2007. "Coarse contingencies and ambiguity," Theoretical Economics, Econometric Society, vol. 2(4), December.
  27. Jacob Sagi, 2006. "What is an ‘endogenous state space’?," Economic Theory, Springer, vol. 27(2), pages 305-320, January.
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