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Subjective probability, confidence, and Bayesian updating


  • Igor Kopylov

    () (University of California, Irvine)


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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    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

    More about this item


    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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