  Potential buyers of a product or service, before making their decisions, tend
to read reviews written by previous consumers. We consider Bayesian consumers
with heterogeneous preferences, who sequentially decide whether to buy an item
of unknown quality, based on previous buyers' reviews. The quality is
multi-dimensional and may occasionally vary over time; the reviews are also
multi-dimensional. In the simple uni-dimensional and static setting, beliefs
about the quality are known to converge to its true value. Our paper extends
this result in several ways. First, a multi-dimensional quality is considered,
second, rates of convergence are provided, third, a dynamical Markovian model
with varying quality is studied. In this dynamical setting the cost of learning
is shown to be small.
