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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 1022, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:10-22
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    File URL: http://wp.econ.ucdavis.edu/10-22.pdf
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    References listed on IDEAS

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    1. Spyros Galanis, 2013. "Unawareness of theorems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 41-73, January.
    2. 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.
    3. 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.
    4. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    5. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
    6. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    7. 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.
    8. 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.
    9. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
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    11. Blume, Lawrence & Easley, David & Halpern, Joseph Y., 2009. "Constructive Decision Theory," Economics Series 246, Institute for Advanced Studies.
    12. 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.
    13. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    14. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
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    18. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
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    Cited by:

    1. repec:eee:jetheo:v:175:y:2018:i:c:p:265-290 is not listed on IDEAS
    2. repec:kap:theord:v:83:y:2017:i:2:d:10.1007_s11238-017-9594-z is not listed on IDEAS
    3. Konrad Grabiszewski, 2015. "Rationalizing epistemic bounded rationality," Theory and Decision, Springer, vol. 78(4), pages 629-637, April.
    4. Karni, Edi & VierÃÿ, Marie-Louise, 2010. ""Reverse Bayesianism": A Choice-Based Theory of Growing Awareness," Queen's Economics Department Working Papers 273757, Queen's University - Department of Economics.
    5. Grabiszewski Konrad, 2016. "On the Rejectability of the Subjective Expected Utility Theory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 437-454, June.
    6. Karni, Edi & Vierø, Marie-Louise, 2017. "Awareness of unawareness: A theory of decision making in the face of ignorance," Journal of Economic Theory, Elsevier, vol. 168(C), pages 301-328.
    7. Wenjun Ma & Burkhard C. Schipper, 2017. "Does exposure to unawareness affect risk preferences? A preliminary result," Theory and Decision, Springer, vol. 83(2), pages 245-257, August.
    8. repec:eee:jetheo:v:176:y:2018:i:c:p:1-54 is not listed on IDEAS
    9. Viero, Marie-Louise, 2017. "An intertemporal model of growing awareness," Queen's Economics Department Working Papers 274714, Queen's University - Department of Economics.
    10. Edi Karni & Marie-Louise Vier?, 2013. ""Reverse Bayesianism": A Choice-Based Theory of Growing Awareness," American Economic Review, American Economic Association, vol. 103(7), pages 2790-2810, December.
    11. Auster, Sarah, 2013. "Asymmetric awareness and moral hazard," Games and Economic Behavior, Elsevier, vol. 82(C), pages 503-521.
    12. Yasuo Sasaki, 2016. "An Equivalence Result on the Reduction of Games with Unawareness," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-27, September.
    13. Ekaterina Svetlova & Henk van Elst, 2014. "Decision-theoretic approaches to non-knowledge in economics," Papers 1407.0787, arXiv.org.
    14. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    15. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    16. repec:eee:gamebe:v:106:y:2017:i:c:p:134-152 is not listed on IDEAS
    17. Karni, Edi & VierÃÿ, Marie-Louise, 2014. "Awareness of Unawareness: A Theory of Decision Making in the Face of Ignorance," Queen's Economics Department Working Papers 274647, Queen's University - Department of Economics.
    18. O'Callaghan, Patrick, 2017. "Axioms for Measuring without mixing apples and Oranges," MPRA Paper 81196, University Library of Munich, Germany.
    19. repec:spr:annopr:v:256:y:2017:i:2:d:10.1007_s10479-016-2266-5 is not listed on IDEAS

    More about this item

    Keywords

    unawareness; awareness; unforeseen contingencies; null; probability zero; subjective probability; Anscombe-Aumann; small worlds;

    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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