# Subjective probability, confidence, and Bayesian updating

## Author

Listed:
• Igor Kopylov

() (University of California, Irvine)

## Abstract

Abstract I define subjective probabilities for an ambiguity averse agent who is given an exogenous information set $$\varDelta$$ Δ containing the true probability law on the state space S. The agent in my model evaluates every uncertain prospect via a mixture of the least favorable scenario in $$\varDelta$$ Δ and her unique subjective belief p. This parametric utility structure is characterized by four standard axioms—order, continuity, monotonicity, and Independence—where the last two conditions are modified via the information set $$\varDelta$$ Δ . Any pair of preferences $$\succeq _1$$ ⪰ 1 and $$\succeq _2$$ ⪰ 2 in my model can be compared in terms of confidence—the weights attached to the subjective beliefs $$p_1$$ p 1 and $$p_2$$ p 2 , respectively. The corresponding behavioral condition extends Epstein’s comparative ambiguity aversion that leaves some rankings $$\succeq _1$$ ⪰ 1 and $$\succeq _2$$ ⪰ 2 unrelated. Moreover, I relax the well-known dynamic consistency principle and characterize the Bayesian updating rule for the belief p conditional on any non-null event in S.

## Suggested Citation

• Igor Kopylov, 2016. "Subjective probability, confidence, and Bayesian updating," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 635-658, October.
• Handle: RePEc:spr:joecth:v:62:y:2016:i:4:d:10.1007_s00199-015-0929-0
DOI: 10.1007/s00199-015-0929-0
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## References listed on IDEAS

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## Citations

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Cited by:

1. repec:eee:jetheo:v:176:y:2018:i:c:p:693-726 is not listed on IDEAS
2. repec:spr:joecth:v:66:y:2018:i:2:d:10.1007_s00199-017-1064-x is not listed on IDEAS
3. Auster, Sarah, 2018. "Robust contracting under common value uncertainty," Theoretical Economics, Econometric Society, vol. 13(1), January.
4. repec:kap:theord:v:83:y:2017:i:1:d:10.1007_s11238-016-9584-6 is not listed on IDEAS
5. repec:eee:proeco:v:200:y:2018:i:c:p:50-67 is not listed on IDEAS

### Keywords

Ambiguity; Bayesian updating; Dynamic consistency; Confidence; Multiple priors; Epsilon contamination;

### JEL classification:

• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
• D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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