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Expanding state space and extension of beliefs

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  • Takashi Hayashi

Abstract

This article provides a simple decision theoretic model in which elements of the world successively enter the decision maker’s scope and the state space expands over time, which is intended to be the closest correspondence to the standard subjective expected utility theory. We propose a dynamic consistency condition that after any expansion of the scope, the preference ranking should remain unchanged over acts to which the expansion is irrelevant. Together with other natural axioms, it characterizes a model in which the decision maker’s belief extends over time in order that the marginal distribution of the new belief induced over the old state space coincides with the old belief. It is extended to encompass both expansion of scope and learning events, and we characterize the model with an additional property that the decision maker’s belief updating follows Bayes’ rule when she learns events. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Takashi Hayashi, 2012. "Expanding state space and extension of beliefs," Theory and Decision, Springer, vol. 73(4), pages 591-604, October.
    • Handle: RePEc:kap:theord:v:73:y:2012:i:4:p:591-604
    DOI: 10.1007/s11238-012-9302-y
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    References listed on IDEAS

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    Cited by:

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    2. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    3. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    4. 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.
    5. Ekaterina Svetlova & Henk van Elst, 2012. "How is non-knowledge represented in economic theory?," Papers 1209.2204, arXiv.org.

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