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Generalized Partition and Subjective Filtration

Author

Listed:
  • David Dillenberger

    (Department of Economics, University of Pennsylvania)

  • Philipp Sadowski

    (Department of Economics, Duke University)

Abstract

We study an individual who faces a dynamic decision problem in which the process of information arrival is unobserved by the analyst, and hence should be identified from observed choice data. An information structure is objectively describable if signals correspond to events of the objective state space. We derive a representation of preferences over menus of acts that captures the behavior of a Bayesian decision maker who expects to receive such signals. The class of information structures that can support such a representation generalizes the notion of a partition of the state space. The representation allows us to compare individuals in terms of the preciseness of their information structures without requiring that they share the same prior beliefs. We apply the model to study an individual who anticipates gradual resolution of uncertainty over time. Both the filtration (the timing of information arrival with the sequence of partitions it induces) and prior beliefs are uniquely identified.

Suggested Citation

  • David Dillenberger & Philipp Sadowski, 2012. "Generalized Partition and Subjective Filtration," PIER Working Paper Archive 12-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:12-036
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    References listed on IDEAS

    as
    1. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 2009. "Temptation-Driven Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 937-971.
    2. Riella, Gil, 2013. "Preference for Flexibility and Dynamic Consistency," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2467-2482.
    3. Gilboa, Itzhak & Postlewaite, Andrew & Schmeidler, David, 2009. "Is It Always Rational To Satisfy Savage'S Axioms?," Economics and Philosophy, Cambridge University Press, vol. 25(3), pages 285-296, November.
    4. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
    5. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, September.
    6. David Dillenberger & Philipp Sadowski & Juan Sebastian Lleras & Norio Takeoka, 2012. "A Theory of Subjective Learning," PIER Working Paper Archive 12-034, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. David Dillenberger & Juan Sebastian Lleras & Philipp Sadowski & Norio Takeoka, 2012. "A Theory of Subjective Learning," Working Papers 12-17, Duke University, Department of Economics.
    8. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    9. Hyogo, Kazuya, 2007. "A subjective model of experimentation," Journal of Economic Theory, Elsevier, vol. 133(1), pages 316-330, March.
    10. David Dillenberger & Juan Sebastian Lleras & Philipp Sadowski & Norio Takeoka, 2012. "A Theory of Subjective Learning," Levine's Working Paper Archive 786969000000000583, David K. Levine.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Resolution of uncertainty; valuing binary bets more; generalized partition; subjective filtration;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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