The Value of Price Discrimination in Large Random Networks

We study the value of price discrimination in large random networks. Recent trends in industry suggest that increasingly firms are using information about social network to offer personalized prices to individuals based upon their positions in the social network. In the presence of positive network externalities, firms aim to increase their profits by offering discounts to influential individuals that can stimulate consumption by other individuals at a higher price. However, the lack of transparency in discriminative pricing can reduce consumer satisfaction and create mistrust. Recent research has focused on the computation of optimal prices in deterministic networks under positive externalities. We would like to answer the question: how valuable is such discriminative pricing? We find, surprisingly, that the value of such pricing policies (increase in profits due to price discrimination) in very large random networks are often not significant. Particularly, for Erdos Renyi random networks, we provide the exact rates at which this value decays in the size of the networks for different ranges of network densities. Our results show that there is a reasonable value of price discrimination for a small class of moderate-sized Erdos-Renyi random networks. We also present a framework to obtain bounds on the value of price discrimination for random networks with general degree distributions and apply the framework to obtain bounds on the value of price discrimination in power-law networks. Our numerical experiments demonstrate our results and suggest that our results are robust to changes in the model of network externalities