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.
Similar content being viewed by others
References
Å gotnes, T., Alechina N.: Full and relative awareness: a decidable logic for reasoning about knowledge of unawareness. Mimeo, University of Nottingham (2007)
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)
Cappé O., Eric M. and Tobias R. (2007). Inference in Hidden Markov Models. Springer, New York
Diaconis P. and Freedman D. (1993). Nonparametric binary regression: a Bayesian approach. Ann. Statist. 21: 2108–2137
Diaconis P. and Freedman D. (1995). Nonparametric binary regression with random covariates. Probability and Math. Stat. 15: 243–273
Feinberg, Y.: Subjective reasoning—games with unawareness. Mimeo, Stanford University (2004)
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)
Hansen L.P. (2007). Beliefs, doubts and learning: the valuation of macroeconomic risk. Am. Econ. Rev. 97: 1–30
Heifetz A., Schipper B.C., Meier M.: Unawareness, beliefs and games. Mimeo (2007)
Hill B. (1986). Some subjective Bayesian considerations in the selection of models. Econom. Rev. 4: 191–246
Klibanoff P., Marinacci M. and Mukerji S. (2005). A smooth model of decision making under ambiguity. Econometrica 73: 1849–1892
Klibanoff, P., Massimo Marinacci and Sujoy Mukerji: Recursive Smooth Ambiguity Preferences. Mimeo (2007)
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)
Li, J.: Dynamic games of complete information with unawareness. Mimeo, University of Pennsylvania (2006)
Modica S. and Rustichini A. (1994). Awareness and partitional information structures. Theory Decis. 37: 107–124
Modica S. and Rustichini A. (1999). Unawareness and partitional information structures. Games. Econ. Behav. 27: 265–298
Poirier D. (1988). Frequentist and subjectivist perspectives on the problem of model building in economics. J. Econ. Perspect. 2: 121–144
Regô, L.C., Halpern, J.: Generalized solution concepts in games with possibly unaware players. Mimeo, Federal University of Pernambuco (2007)
Rydén T. (1997). On recursive estimation for hidden markov models. Stoch. Processes Appl. 66: 79–96
Sadzik, T.: Knowledge, awareness and probabilistic beliefs. Mimeo, Graduate School of Business. Stanford University (2006)
Schipper, B.: The unawareness bibliography. http://www.econ.ucdavis.edu/faculty/schipper (2007)
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)
Weitzman, M.: Prior sensitive expectations and asset return puzzles. Am. Econ. Rev. (2007, Forthcoming)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Modica, S. Unawareness, priors and posteriors. Decisions Econ Finan 31, 81–94 (2008). https://doi.org/10.1007/s10203-007-0078-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10203-007-0078-4