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IMA Journal of Management Mathematics Advance Access published online on May 28, 2009
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpp003
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© The authors 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Word-of-mouth and dynamical inhomogeneous markets: an efficiency measure and optimal sampling policies for the pre-launch stage

Elena Agliari

Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany

Raffaella Burioni{dagger} and Davide Cassi

Dipartimento di Fisica, Università degli Studi di Parma and INFN Gruppo Collegato di Parma, Via G.P. Usberti 7/A, 43100 Parma, Italy

Franco Maria Neri

Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK

{dagger} Email: raffaella.burioni{at}fis.unipr.it

Received on 9 October 2008. Accepted on 28 April 2009.

An important assumption lying behind innovation diffusion models and word-of-mouth (WOM) 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 ‘microlevel’ process for the diffusion of an innovative product based on a WOM 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 prelaunch 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 WOM; additional advertising is absent. The authors find an unexpected general failure of the WOM 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 prelaunch 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.

Keywords: diffusion models; simulations; random walks; word of mouth; prelaunch strategies


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