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Awareness-Dependent Subjective Expected Utility

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  • Burkhard Schipper

    (Department of Economics, University of California Davis)

Abstract

We develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2011a) as primitives in the Anscombe-Aumann approach to subjective expected utility. We observe that a decision maker is unaware of an event if and only if her choices reveal that the event is ``null'' and the negation of the event is ``null''. Moreover, we characterize ``impersonal'' expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. We discuss in what sense probability zero can model unawareness.

Suggested Citation

  • Burkhard Schipper, 2011. "Awareness-Dependent Subjective Expected Utility," Working Papers 264, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:264
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    References listed on IDEAS

    as
    1. Martin Meier & Burkhard C. Schipper, 2014. "Speculative trade under unawareness: the infinite case," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 147-160, October.
    2. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
    3. Heinsalu, Sander, 2012. "Equivalence of the information structure with unawareness to the logic of awareness," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2453-2468.
    4. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-924, July.
    5. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    6. Burkhard Schipper, 2011. "Preference-Dependent Unawareness," Working Papers 116, University of California, Davis, Department of Economics.
    7. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    8. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    9. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2008. "A canonical model for interactive unawareness," Games and Economic Behavior, Elsevier, vol. 62(1), pages 304-324, January.
    10. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    11. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
    12. Blume, Lawrence & Easley, David & Halpern, Joseph Y., 2021. "Constructive decision theory," Journal of Economic Theory, Elsevier, vol. 196(C).
    13. Morris, Stephen, 1996. "The Logic of Belief and Belief Change: A Decision Theoretic Approach," Journal of Economic Theory, Elsevier, vol. 69(1), pages 1-23, April.
    14. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    15. Simon Grant & John Quiggin, 2013. "Inductive reasoning about unawareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 717-755, November.
    16. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    17. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    18. Burkhard Schipper, 2011. "Preference-Dependent Unawareness," Working Papers 269, University of California, Davis, Department of Economics.
    19. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
    20. Burkhard C. Schipper & Oliver Board & Kim-Sau Chung, 2009. "Two Models of Unawareness: Comparing the object-based and subjective-state-space approaches," Working Papers 93, University of California, Davis, Department of Economics.
    21. Oliver Board, 2008. "Object-Based Unawareness: Theory and Applications," Working Paper 378, Department of Economics, University of Pittsburgh, revised Mar 2009.
    22. Galanis, Spyros, 2007. "Unawareness of theorems," Discussion Paper Series In Economics And Econometrics 51816, Economics Division, School of Social Sciences, University of Southampton.
    23. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    24. Jing Li, 2008. "A Note on Unawareness and Zero Probability," PIER Working Paper Archive 08-022, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    25. David S. Ahn & Haluk Ergin, 2010. "Framing Contingencies," Econometrica, Econometric Society, vol. 78(2), pages 655-695, March.
    26. Oliver Board & Kim-Sau Chung & Burkhard C. Schipper, 2008. "Two Models of Unawareness," Working Paper 379, Department of Economics, University of Pittsburgh, revised Mar 2009.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    unawareness; awareness; unforeseen contingencies; null; probability zero; subjective probability; Anscombe-Aumann; small worlds;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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