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Simple axioms for countably additive subjective probability

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  • Kopylov, Igor

Abstract

This paper refines Savage's theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow's (1970) Monotone Continuity. Second, I relax Savage's primitives: in my framework, the class of events need not be a [sigma]-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory's unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.

Suggested Citation

  • Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:867-876
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    References listed on IDEAS

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    1. Peter Wakker, 1993. "Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 487-493.
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    Cited by:

    1. Alon, Shiri & Lehrer, Ehud, 2014. "Subjective multi-prior probability: A representation of a partial likelihood relation," Journal of Economic Theory, Elsevier, vol. 151(C), pages 476-492.
    2. Kopylov, Igor, 2016. "Canonical utility functions and continuous preference extensions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 32-37.
    3. Harvey, Charles M. & Ă˜sterdal, Lars Peter, 2012. "Discounting models for outcomes over continuous time," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 284-294.
    4. Kopylov, Igor, 2010. "Unbounded probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 113-118, September.
    5. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    6. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    7. Hara, Kazuhiro, 2016. "Characterization of stationary preferences in a continuous time framework," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 34-43.
    8. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    9. Spinu, Vitalie & Wakker, Peter P., 2013. "Expected utility without continuity: A comment on Delbaen et al. (2011)," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 28-30.

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