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Purely subjective extended Bayesian models with Knightian unambiguity

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  • Xiangyu Qu

Abstract

This paper provides a model of belief representation in which ambiguity and unambiguity are endogenously distinguished in a purely subjective setting where objects of choices are, as usual, maps from states to consequences. Specifically, I first extend the maxmin expected utility theory and get a representation of beliefs such that the probabilistic beliefs over each ambiguous event are represented by a non-degenerate interval, while the ones over each unambiguous event are represented by a number. I then consider a class of the biseparable preferences. Two representation results are achieved and can be used to identify the unambiguity in the context of the biseparable preferences. Finally a subjective definition of ambiguity is suggested. It provides a choice theoretic foundation for the Knightian distinction between ambiguity and unambiguity. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Xiangyu Qu, 2015. "Purely subjective extended Bayesian models with Knightian unambiguity," Theory and Decision, Springer, vol. 79(4), pages 547-571, December.
    • Handle: RePEc:kap:theord:v:79:y:2015:i:4:p:547-571
    DOI: 10.1007/s11238-015-9489-9
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    More about this item

    Keywords

    Knightian distinction; Maxmin expected utility; Biseparable preference; Unambiguous event; D80; D81;
    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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