Corrigendum to “Evaluating Ambiguous Random Variables from Choquet to Maxmin Expected Utility" [Journal of Economic Theory 192 (2021) 105129]. Journal of Economic Theory Volume 227, June 2025, Article 106034.

Gul and Pesendorfer (2021, GP henceforth) introduce a theory of belief updating for ambiguous random variables. In their model, the decision maker’s uncertainty is described by a totally monotone capacity π, which is updated by first forming a so-called proxy capacity πP, which in general depends on the information partition P. The proxy is then updated by Bayes’ rule. GP note that this procedure can be interpreted as a modified version of prior-by-prior updating: Instead of updating every prior in the core of the capacity π, the decision maker considers and updates only a subset of the priors, namely those in the core of the proxy πP.
 

GP characterize the core of the proxy capacity πPin terms of the Shapley value of the cooperative game corresponding to the capacity π. We show by counterexample that this characterization is incorrect. Thus, GP’s Corollary 2 does not hold as stated. After presenting the example, we explain how the result should be corrected.  We also give some simple characterizations of the core of πP, which show that the core is in general a subset of the set identified by GP.