Abstract
Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130:78–94, 2006). In particular, we show that subjective-state-space models (henceforth HMS structures) can be embedded within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse.
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Acknowledgements
We thank Eddie Dekel, Joe Halpern, Aviad Heifetz, and Ming Li for helpful discussions. Burkhard gratefully acknowledges financial support from the NSF SES-0647811.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Board, O.J., Chung, KS. & Schipper, B.C. Two models of unawareness: comparing the object-based and the subjective-state-space approaches. Synthese 179 (Suppl 1), 13–34 (2011). https://doi.org/10.1007/s11229-010-9850-z
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DOI: https://doi.org/10.1007/s11229-010-9850-z