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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, vol. 76(2), pages 242-271, October.
  2. Martin Meier & Burkhard C. Schipper & Aviad Heifetz, 2009. "Dynamic Unawareness and Rationalizable Behavior," Working Papers 910, University of California, Davis, Department of Economics.
  3. 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.
  4. Sujoy Mukerji, 1996. "Understanding the nonadditive probability decision model (*)," Economic Theory, Springer, vol. 9(1), pages 23-46.
  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. Martin Meier & Burkhard C. Schipper, 2013. "Speculative Trade under Unawareness: The Infinite Case," Working Papers 102, University of California, Davis, Department of Economics.
  7. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
  8. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  9. Ewerhart, Christian, 2001. "Heterogeneous Awareness and the Possibility of Agreement," Sonderforschungsbereich 504 Publications 01-30, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  10. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  11. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  12. Youichiro Higashi & Kazuya Hyogo, 2012. "Lexicographic expected utility with a subjective state space," Economic Theory, Springer, vol. 49(1), pages 175-192, January.
  13. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
  14. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
  15. Salvatore Modica & J.-Marc Tallon & Aldo Rustichini, 1998. "Unawareness and bankruptcy: A general equilibrium model," Economic Theory, Springer, vol. 12(2), pages 259-292.
  16. Jacob Sagi, 2006. "What is an ‘endogenous state space’?," Economic Theory, Springer, vol. 27(2), pages 305-320, January.
  17. Paolo Ghirardato, 2001. "Coping with ignorance: unforeseen contingencies and non-additive uncertainty," Economic Theory, Springer, vol. 17(2), pages 247-276.
  18. Joseph Y. Halpern, 2000. "Alternative Semantics for Unawareness," Game Theory and Information 0004010, EconWPA.
  19. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  20. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
  21. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
  22. 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.
  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, edition 1, volume 1, number 0262541599, December.
  24. Aldo Rustichini, 2002. "Preference for flexibility in infinite horizon problems," Economic Theory, Springer, vol. 20(4), pages 677-702.
  25. repec:ecl:ucdeco:09-20 is not listed on IDEAS
  26. Epstein, Larry G. & Marinacci, Massimo & Seo, Kyoungwon, 2007. "Coarse contingencies and ambiguity," Theoretical Economics, Econometric Society, vol. 2(4), December.
  27. 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.
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Citations

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Cited by:
  1. Schipper, Burkhard C, 2010. "Revealed Unawareness," MPRA Paper 21491, University Library of Munich, Germany.
  2. Burkhard Schipper, 2011. "Awareness-Dependent Subjective Expected Utility," Working Papers 1022, University of California, Davis, Department of Economics.
  3. 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.
  4. Sarah Auster, 2012. "Asymmetric Awareness and Moral Hazard," Economics Working Papers ECO2012/23, European University Institute.
  5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2008. "A canonical model for interactive unawareness," Games and Economic Behavior, Elsevier, vol. 62(1), pages 304-324, January.
  6. Auster, Sarah, 2013. "Asymmetric awareness and moral hazard," Games and Economic Behavior, Elsevier, vol. 82(C), pages 503-521.
  7. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2009. "Unawareness, Beliefs and Speculative Trade," MPRA Paper 18437, University Library of Munich, Germany.
  8. 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.
  9. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
  10. 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.
  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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