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Savage's Theorem Under Changing Awareness

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  • Dietrich, Franz

Abstract

This paper proposes a simple unified framework of changing awareness, addressing both outcome and (nature) state awareness, and both how fine and how exhaustive the awareness is. Six axioms characterize an (essentially unique) expected-utility representation of preferences, in which utilities and probabilities are revised systematically under changes in awareness. Revision is governed by three well-defined rules: (R1) certain utilities are transformed affinely, (R2) certain probabilities are transformed proportionally, and (R3) certain (`objective') probabilities are preserved. Rule R2 parallels Karni and Viero's (2013) 'reverse Bayesianism' and Ahn and Ergin's (2010) 'partition-dependence'. Savage's (1954) theorem emerges in the special case of fixed awareness. The theorem draws mathematically on Kopylov (2007), Niiniluoto (1972) and Wakker (1981).

Suggested Citation

  • Dietrich, Franz, 2016. "Savage's Theorem Under Changing Awareness," MPRA Paper 71306, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:71306
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    References listed on IDEAS

    as
    1. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    2. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    3. 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.
    4. 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.
    5. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    6. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    7. Brian Hill, 2010. "Awareness Dynamics," Post-Print hal-00521801, HAL.
    8. David S. Ahn & Haluk Ergin, 2010. "Framing Contingencies," Econometrica, Econometric Society, vol. 78(2), pages 655-695, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Decision under uncertainty; outcome unawareness versus state unawareness; non-refinement versus non-exhaustiveness; utility revision versus probability revision;

    JEL classification:

    • 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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