Things become more complicated when we do not want to assume that the
true values of the uncertain attributes are perceived among consumers as being
mutually independent: in many real-world situations, uncertain attributes
like price may for example be (perceived to be) positively correlated with uncertain
quality-related attributes, as a higher price may signal higher quality of the
good (e.g. Wolinsky, 1983; Milgrom and Roberts, 1986). In such cases of mutual
dependency among uncertain attributes, the benefit of searching for information
concerning on one of these attributes will generally differ from what models
assuming independence across attributes would predict. Take for example the
situation where price is perceived among consumers to positively correlate with
quality. Information about price will then also be perceived to contain additional
(indirect) information concerning quality. As a result, its value for consumers will
be higher than if price were perceived to be uncorrelated with quality. Also, the
value of subsequent information concerning uncertain quality-related attributes
will be lower than in situations where price-information does not provide indirect
quality-related information. The value of information in situations where
several uncertain attributes are perceived to be correlated can be modelled using
Bayesian Belief Networks (Pearl, 1988), where consumer beliefs are modelled as
a coherent set of conditional probabilities. However, incorporating the notion
of mutual dependencies across uncertain attributes will generally lead to more
complex and less tractable models.