Efficient Learning under Ambiguous Information

Department of Economics and Decision Sciences
Speaker : Mira Frick (Yale Univ.)
Room T-009
 

Abstract :

“We provide a systematic approach to compare different belief-updating rules under
ambiguity, based on analyzing their performance in learning settings. We consider a
decision-maker (DM) with maxmin expected utility preferences who observes many
signals about an unknown state of the world, and then solves a decision problem based
on her updated beliefs. Capturing signal ambiguity, the DM perceives a set of possible
signal structures. A belief-updating rule maps sequences of signals to sets of posteriors
about the state, and the DM chooses optimally based on her worst-case posterior. We
measure the learning efficiency of each updating rule by considering the DM’s induced
worst-case expected payoff, evaluated from an ex-ante perspective. Thus, updating rules
with higher learning efficiency can be viewed as displaying less dynamic inconsistency.
We provide a simple characterization of the learning efficiency of each updating rule.
This has the following main implications. First, in stationary environments (i.e., when
signal draws are conditionally i.i.d.), we show that learning efficiency is maximal if (and,
in a sense, only if) the DM uses maximum-likelihood updating; in contrast, the widely
used full-Bayesian updating rule is generically (potentially highly) inefficient. Second, in
non-stationary environments (i.e., when signal structures can vary over time), we show
that learning efficiency is maximal if (and, in a sense, only if) the DM uses a maximum likelihood
updating rule that (mis)perceives the environment to be stationary.