Abstract
We consider the problem of deriving optimal marketing policies for the spread of innovations in a social network. We seek to compute policies that account for i) endogenous network influences, ii) the presence of competitive firms, that also wish to influence the network, and iii) possible uncertainties in the network model. Contrary to prior work in optimal advertising, which also accounts for network influences, we assume a dynamical model of preferences
and we compute optimal policies for either a finite or infinite horizon. The optimal policies are related to and extend priorly introduced notions of centrality measures usually considered in sociology. We also compute robust optimal policies for the case of misspecified dynamics or uncertainties which can be modeled as external disturbances of the nominal dynamics. We show that the optimization exhibits a certainty equivalence property, i.e., the optimal values of the control variables are the same as if there were no uncertainty. Finally, we investigate the scenario where a competitive firm also tries to influence the network. In this case, robust optimal solutions are computed in the form of i) Nash and Stackelberg solutions, and ii) max-min solutions.