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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

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    1. Dietrich, Franz & List, Christian, 2016. "Reason-Based Choice And Context-Dependence: An Explanatory Framework," Economics and Philosophy, Cambridge University Press, vol. 32(2), pages 175-229, July.
    2. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    3. repec:hal:wpaper:halshs-01249632 is not listed on IDEAS
    4. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    5. 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.
    6. Dietrich, Franz & List, Christian, 2016. "Mentalism Versus Behaviourism In Economics: A Philosophy-Of-Science Perspective," Economics and Philosophy, Cambridge University Press, vol. 32(2), pages 249-281, July.
    7. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    8. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    9. Brian Hill, 2010. "Awareness Dynamics," Post-Print hal-00521801, HAL.
    10. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    11. 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.
    12. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831, Elsevier.
    13. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    14. 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)

    Citations

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    Cited by:

    1. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    2. Vierø, Marie-Louise, 2021. "An intertemporal model of growing awareness," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Boissonnet, Niels & Ghersengorin, Alexis & Gleyze, Simon, 2020. "Revealed Deliberate Preference Changes," MPRA Paper 101756, University Library of Munich, Germany.
    4. Christoph K. Becker & Tigran Melkonyan & Eugenio Proto & Andis Sofianos & Stefan T. Trautmann, 2020. "Reverse Bayesianism: Revising Beliefs in Light of Unforeseen Events," CESifo Working Paper Series 8662, CESifo.
    5. Grant Simon & Guerdjikova Ani & Quiggin John, 2021. "Ambiguity and Awareness: A Coherent Multiple Priors Model," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 571-612, June.
    6. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    7. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    8. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.
    9. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).

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    More about this item

    Keywords

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

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