A Formalization of the Greater Fools Theory with Dynamic Epistemic Logic

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10455)


The greater fools explanation of financial bubbles says that traders are willing to pay more for an asset than they deem it worth, because they anticipate they might be able to sell it to someone else for an even higher price. As agents’ beliefs about other agents’ beliefs are at the heart of the greater fools theory, this paper comes to formal terms with the theory by translating the phenomenon into the language and models of dynamic epistemic logic. By presenting a formalization of greater fools reasoning, structural insights are obtained pertaining to the structure of its higher-order content and the role of common knowledge.


  1. 1.
    Abreu, D., Brunnermeier, M.K.: Bubbles and crashes. Econometrica 71(1), 173–204 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Allen, F., Morris, S., Postlewaite, A.: Finite bubbles with short sale constraints and asymmetric information. J. Econ. Theor. 61, 206–229 (1993)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baltag, A., Christoff, Z., Hansen, J.U., Smets, S.: Logical models of informational cascades. In: van Benthem, J., Liu, F. (eds.) Logic Across the University: Foundations and Applications - Proceedings of the Tsinghua Logic Conference, vol. 47, pp. 405–432. College Publications, London (2013)Google Scholar
  4. 4.
    Baltag, A., Smets, S.: Dynamic belief revision over multi-agent plausibility models. In: Bonanno, G., Wooldridge, M. (eds.) Proceedings of the 7th Conference on Logic and the Foundations of Game and Decision (LOFT 2006), pp. 11–24. University of Liverpool (2006)Google Scholar
  5. 5.
    Barlevy, G.: Bubbles and fools. Econ. Perspect. 39(2), 54–76 (2015)Google Scholar
  6. 6.
    Brunnermeier, M.K.: Asset Pricing Under Asymmetric Information: Bubbles, Crashes, Technical Analysis and Herding. Oxford University Press, New York (2001)CrossRefGoogle Scholar
  7. 7.
    Brunnermeier, M.K.: Bubbles, 2nd edn. In New Palgrave Dictionary of Economics. Palgrave Macmillan, London (2008)zbMATHGoogle Scholar
  8. 8.
    Conlon, J.R.: Simple finite horizon bubbles robust to higher order knowledge. Econometrica 72(3), 927–936 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dégremont, C., Roy, O.: Agreement theorems in dynamic-epistemic logic. J. Philos. Logic 41, 735–764 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    De Long, J.B., Shleifer, A., Summers, L.H., Waldmann, R.J.: Noise trader risk in financial markets. J. Polit. Econ. 98, 703–738 (1990)CrossRefGoogle Scholar
  11. 11.
    Demey, L.: Agreeing to disagree in probabilistic dynamic epistemic logic. Synthese 191, 409–438 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Fama, E.F.: The behavior of stock-market prices. J. Bus. 38, 34–105 (1965)CrossRefGoogle Scholar
  13. 13.
    Gerbrandy, J., Groeneveld, W.: Reasoning about information change. J. Logic Lang. Inform. 6, 147–169 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kindleberger, C.P., Aliber, R.Z.: Manias, Panics, and Crashes: a history of financial crises, 5th edn. John Wiley and Sons Inc., USA (2005)CrossRefGoogle Scholar
  15. 15.
    Kooi, B.: Probabilistic dynamic epistemic logic. J. Logic Lang. Inform. 12, 381–408 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Levine, S.S., Zajac, E.J.: The institutional nature of price bubbles. SSRN Electroni. J. 11(1), 109–126 (2007)Google Scholar
  17. 17.
    Rendsvig, R.K.: Aggregated beliefs and informational cascades. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2013. LNCS, vol. 8196, pp. 337–341. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40948-6_29 CrossRefGoogle Scholar
  18. 18.
    Tirole, J.: On the possibility of speculation under rational expectations. Econometrica 50(5), 1163–1181 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Vogel, H.L.: Financial Market: Bubbles and Crashes. Cambridge University Press, New York (2010)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Center for Information and Bubble StudiesUniversity of CopenhagenCopenhagenDenmark

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