Optimal influence budget allocation for viral marketing using a multiple virus SIS model
Résumé
In the problem addressed in this paper, a firm proposes a service/product to customers that are spread over several geographical regions (e.g., countries, provinces, or states). Each region has its own characteristics in terms of service propagation and is subject to the influence of several firms. The service propagation is modeled by a (marketing) virus process whose effective spreading rate depends on the influence exerted by the firms. The considered overall dynamical system thus involves multiple competing firms whose individual influence over their customers is modeled by a virus and multiple regions. One of the goals of the paper is to know how a firm should allocate its budget among the regions to maximize its market share. The corresponding optimization problem is studied by assuming a Susceptible-Infected-Susceptible (SIS) multiple virus model. In this setting, it is shown under which conditions the so-called "winner takes all" viral marketing strategy is optimal. More generally, the best strategy is derived and its performance is shown to outperform the uniform allocation strategy and advanced strategies like those derived from a Colonel Blotto approach.
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