  An important assumption lying behind innovation diffusion models and
word-of-mouth processes is that of homogeneous mixing: at any time, the
individuals making up the market are uniformly distributed in space. When the
geographical parameters of the market, such as its area extension, become
important, the movement of individuals must be explicitly taken into account.
The authors introduce a model for a "micro-level" process for the diffusion of
an innovative product, based on a word-of-mouth mechanism, and they explicitly
consider the inhomogeneity of markets and the spatial extent of the
geographical region where the process takes place. This results in an
unexpected behaviour of macro (aggregate) level measurable quantities. The
authors study the particular case of the pre-launch stage, where a product is
first presented to the market through free sample distribution. The first
triers of the samples then inform the other potential customers via
word-of-mouth; additional advertising is absent. The authors find an unexpected
general failure of the word-of-mouth mechanism for high market densities and
they obtain quantitative results for the optimal sampling policy. By
introducing a threshold to discriminate between individuals who will purchase
and those who will not purchase according to their individual goodwill, they
calculate the length of the pre-launch campaign and the final goodwill as a
function of the firm's expenditure. These results are applied to a set of major
US urban areas.
