Revealed Ambiguity and Its Consequences: Updating

Abstract

results in this paper were earlier circulated as part of a working paper titled "Ambiguity from the Differential Viewpoint" (Caltech Social Sciences Working Paper Number 1130, April 2002. We are grateful to Marciano Siniscalchi for many conversations on the topic of this paper.

Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News

“…The typical interpretation is that an act is a "bet" which returns, in every state of the world, a specific consequence in X, e.g., an amount of money. 6 See, among others, Gilboa and Schmeidler (1993); Epstein and Le Breton (1993); Epstein and Schneider (2003); Maccheroni, Marinacci, and Rustichini (2006); Siniscalchi (2011); Hanany and Klibanoff (2007); Ghirardato, Maccheroni, and Marinacci (2008); Hanany and Klibanoff (2009); and Epstein and Schneider (2007). The latter discusses a form of hypothesis testing for updating multiple priors.…”

Dynamic objective and subjective rationality

“…The equivalence between dynamic consistency and the prior‐by‐prior updating rule in Bewley's model was previously discussed by Bewley () and Epstein and Le Breton ( ) as a kind of “folk theorem.” Formally, the relationship between our model and GMMS is similar to the relationship between GMM ( ) and GMM ( ). We also note that while GMM ( ) assume consequentialism (as does Ghirardato 2002 ), we derive it from our mild assumptions (Proposition in the Appendix). Furthermore, there seems to be no straightforward way to apply the arguments in GMM ( ) to derive foundations for prior‐by‐prior updating of maxmin expected utility in the two‐preference setting (Theorem ).…”

“…Ghirardato, Maccheroni, and Marinacci (GMM , ) consider a model with a single binary relation that may exhibit nonneutrality to ambiguity and induce a subrelation called unambiguous preference that has a Bewley representation. By requiring dynamic consistency and consequentialism, GMM ( ) show that an unambiguous preference must be updated in accordance with full Bayesian updating.…”

“…Ghirardato, Maccheroni, and Marinacci (GMM , ) consider a model with a single binary relation that may exhibit nonneutrality to ambiguity and induce a subrelation called unambiguous preference that has a Bewley representation. By requiring dynamic consistency and consequentialism, GMM ( ) show that an unambiguous preference must be updated in accordance with full Bayesian updating. The equivalence between dynamic consistency and the prior‐by‐prior updating rule in Bewley's model was previously discussed by Bewley () and Epstein and Le Breton ( ) as a kind of “folk theorem.” Formally, the relationship between our model and GMMS is similar to the relationship between GMM ( ) and GMM ( ).…”

“…By requiring dynamic consistency and consequentialism, GMM ( ) show that an unambiguous preference must be updated in accordance with full Bayesian updating. The equivalence between dynamic consistency and the prior‐by‐prior updating rule in Bewley's model was previously discussed by Bewley () and Epstein and Le Breton ( ) as a kind of “folk theorem.” Formally, the relationship between our model and GMMS is similar to the relationship between GMM ( ) and GMM ( ). We also note that while GMM ( ) assume consequentialism (as does Ghirardato 2002 ), we derive it from our mild assumptions (Proposition in the Appendix).…”