The Value of Price Discrimination in Large Social Networks

We study the value of price discrimination in large social 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 may reduce consumer satisfaction and create mistrust. Recent research focuses on the computation of optimal prices in deterministic networks under positive externalities. We want to answer the question of how valuable such discriminative pricing is. We find, surprisingly, that the value of such pricing policies (increase in profits resulting from price discrimination) in very large random networks are often not significant. Particularly, for Erdös–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 nonnegligible value of price discrimination for a small class of moderate-sized Erdös–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.