Advertisement

Decisions in Economics and Finance

, Volume 31, Issue 2, pp 81–94 | Cite as

Unawareness, priors and posteriors

  • Salvatore ModicaEmail author
Article

Abstract

This note contains first thoughts on awareness of unawareness in a simple dynamic context where a decision situation is repeated over time. The main consequence of increasing awareness is that the model the decision maker uses, and the prior which it contains, becomes richer over time. The decision maker is prepared to this change, and we show that if a projection-consistency axiom is satisfied unawareness does not affect the value of her estimate of a payoff-relevant conditional probability (although it may weaken confidence in such estimate). Probability-zero events however, pose a challenge to this axiom, and if that fails, even estimate values will be different if the decision maker takes unawareness into account. In examining evolution of knowledge about relevant variable through time, we distinguish between transition from uncertainty to certainty and from unawareness to certainty directly, and argue that new knowledge may cause posteriors to jump more if it is also new awareness. Some preliminary considerations on convergence of estimates are included.

Keywords

Awareness of Unawareness Model Uncertainty 

JEL Classification

D83 C11 

Mathematics Subject Classification (2000)

91B06 91B44 62C10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Å gotnes, T., Alechina N.: Full and relative awareness: a decidable logic for reasoning about knowledge of unawareness. Mimeo, University of Nottingham (2007)Google Scholar
  2. Board, O., Chung, K.S.: Object-based unawareness. In: Bonanno, G., van der Hoek, W., Woolridge, M. (eds.) Logic and the Foundations of Game and Decision Theory, Proceedings of the 7th Conference (2006)Google Scholar
  3. Cappé O., Eric M. and Tobias R. (2007). Inference in Hidden Markov Models. Springer, New York Google Scholar
  4. Diaconis P. and Freedman D. (1993). Nonparametric binary regression: a Bayesian approach. Ann. Statist. 21: 2108–2137 CrossRefGoogle Scholar
  5. Diaconis P. and Freedman D. (1995). Nonparametric binary regression with random covariates. Probability and Math. Stat. 15: 243–273 Google Scholar
  6. Feinberg, Y.: Subjective reasoning—games with unawareness. Mimeo, Stanford University (2004)Google Scholar
  7. Halpern, J., Regô L.C.: Extensive games with possibly unaware players. In: Proceedings 5th International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 744–751 (2006)Google Scholar
  8. Hansen L.P. (2007). Beliefs, doubts and learning: the valuation of macroeconomic risk. Am. Econ. Rev. 97: 1–30 CrossRefGoogle Scholar
  9. Heifetz A., Schipper B.C., Meier M.: Unawareness, beliefs and games. Mimeo (2007)Google Scholar
  10. Hill B. (1986). Some subjective Bayesian considerations in the selection of models. Econom. Rev. 4: 191–246 CrossRefGoogle Scholar
  11. Klibanoff P., Marinacci M. and Mukerji S. (2005). A smooth model of decision making under ambiguity. Econometrica 73: 1849–1892 CrossRefGoogle Scholar
  12. Klibanoff, P., Massimo Marinacci and Sujoy Mukerji: Recursive Smooth Ambiguity Preferences. Mimeo (2007)Google Scholar
  13. Lehrer, E., Smorodinsky, R.: Merging and Learning, in Statistics, Probability and Game Theory: Papers in Honor of David Blackwell. Ferguson, T., Shapley, L., MacQueen, J. (eds.) IMS Lecture Notes—Monograph Series, vol 30, pp. 147–168 (1996)Google Scholar
  14. Li, J.: Dynamic games of complete information with unawareness. Mimeo, University of Pennsylvania (2006)Google Scholar
  15. Modica S. and Rustichini A. (1994). Awareness and partitional information structures. Theory Decis. 37: 107–124 CrossRefGoogle Scholar
  16. Modica S. and Rustichini A. (1999). Unawareness and partitional information structures. Games. Econ. Behav. 27: 265–298 CrossRefGoogle Scholar
  17. Poirier D. (1988). Frequentist and subjectivist perspectives on the problem of model building in economics. J. Econ. Perspect. 2: 121–144 Google Scholar
  18. Regô, L.C., Halpern, J.: Generalized solution concepts in games with possibly unaware players. Mimeo, Federal University of Pernambuco (2007)Google Scholar
  19. Rydén T. (1997). On recursive estimation for hidden markov models. Stoch. Processes Appl. 66: 79–96 CrossRefGoogle Scholar
  20. Sadzik, T.: Knowledge, awareness and probabilistic beliefs. Mimeo, Graduate School of Business. Stanford University (2006)Google Scholar
  21. Schipper, B.: The unawareness bibliography. http://www.econ.ucdavis.edu/faculty/schipper (2007)
  22. Sillari, G.: Models of awareness. In: Bonanno, G., van der Hoek, W., Woolridge, M. (eds.) Logic and the Foundations of Game and Decision Theory, Proceedings of the 7th Conference (2006)Google Scholar
  23. Weitzman, M.: Prior sensitive expectations and asset return puzzles. Am. Econ. Rev. (2007, Forthcoming)Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Facoltà di EconomiaPalermoItaly

Personalised recommendations