Stochastic optimization on social networks with application to service pricing

In this paper we develop a combined simulation and optimization approach for solving difficult decision problems on complex dynamic networks. For a specific reference problem we consider a telecommunication service provider who offers a telecommunication service to a market with network effects. More particularly, the service consumption of an individual user depends on both idiosyncratic characteristics and the popularity of this service among the customer’s immediate neighborhood. Both the social network and the individual user preferences are largely heterogeneous and changing over time. In addition the service provider’s decisions are made in absence of perfect knowledge about user preferences. The service provider pursues the strategy of stimulating the demand by offering differentiated prices to the customers. For finding the optimal pricing we apply a stochastic quasi-gradient algorithm that is integrated with a simulation model that drives the evolution of the network and user preferences over time. We show that exploiting the social network structure and implementing differentiated pricing can substantially increase the revenues of a service provider operating on a social network. More generally, we show that stochastic gradient methods represent a powerful methodology for the optimization of decisions in social networks.