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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. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
  2. Youichiro Higashi & Kazuya Hyogo, 2012. "Lexicographic expected utility with a subjective state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 175-192, January.
  3. 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, December.
  4. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  5. 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.
  6. Martin Meier & Burkhard C. Schipper & Aviad Heifetz, 2009. "Dynamic Unawareness and Rationalizable Behavior," Working Papers 910, University of California, Davis, Department of Economics.
  7. Ewerhart, Christian, 2001. "Heterogeneous Awareness and the Possibility of Agreement," Sonderforschungsbereich 504 Publications 01-30, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  8. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
  9. repec:ecl:ucdeco:09-20 is not listed on IDEAS
  10. 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.
  11. Jacob Sagi, 2006. "What is an ‘endogenous state space’?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 305-320, January.
  12. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2009. "Unawareness, Beliefs and Speculative Trade," MPRA Paper 18437, University Library of Munich, Germany.
  13. Salvatore Modica & Aldo Rustichini & Jean-Marc Tallon, 1998. "Unawareness and bankruptcy: A general equilibrium model," Post-Print halshs-00499386, HAL.
  14. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  15. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
  16. 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.
  17. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  18. 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.
  19. Martin Meier & Burkhard C. Schipper, 2013. "Speculative Trade under Unawareness: The Infinite Case," Working Papers 102, University of California, Davis, Department of Economics.
  20. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
  21. Paolo Ghirardato, 2001. "Coping with ignorance: unforeseen contingencies and non-additive uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(2), pages 247-276.
  22. 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.
  23. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
  24. Aldo Rustichini, 2002. "Preference for flexibility in infinite horizon problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 677-702.
  25. Epstein, Larry G. & Marinacci, Massimo & Seo, Kyoungwon, 2007. "Coarse contingencies and ambiguity," Theoretical Economics, Econometric Society, vol. 2(4), December.
  26. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
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