# Purely subjective extended Bayesian models with Knightian unambiguity

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## 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.

### Keywords

Knightian distinction Maxmin expected utility Biseparable preference Unambiguous event### JEL Classification

D80 D81## Notes

### Acknowledgments

I am deeply indebted to David Schmeidler for inspiration, guidance, and support. I am also thankful for Yaron Azieli, Chew Soo Hong, and Ani Guerdjikova for helpful discussion. This research was supported by ANR and Labex.

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