We build upon previous models for differential pricing in social networks and fair price discrimination in markets, considering a setting in which multiple units of a single product must be sold to selected buyers so as to maximize the seller's revenue or the social welfare, while limiting the differences of the prices offered to social neighbors. We first consider the case of general social graph topologies, and provide optimal or nearly-optimal hardness and approximation results for the related optimization problems under various meaningful assumptions, including the inapproximability within any constant factor on the achievable revenue under the unique game conjecture. Then, we focus on topologies that are typical of social networks. Namely, we consider graphs where the node degrees follow a power-law distribution, and show that it is possible to obtain constant or good approximations for the seller's revenue maximization with high probability, thus improving upon the general case.

Discriminatory pricing policies, even if at first glance can be perceived as unfair, are widespread. In fact, pricing differences for the same item among different national markets are common, or forms of discrimination based on the time of purchase, like in tickets' sales. In this work we propose a framework for capturing the setting of ``fair'' discriminatory pricing and study its application to multi-unit markets, in which many copies of the same item are on sale. Our model is able to incorporate the fundamental discrimination settings proposed in the literature, by expressing individual buyers constraints for assigning prices by means of a social relationship graph, modeling the information that each buyer can acquire about the prices assigned to the other buyers. After pointing out the positive effects of fair price discrimination, we investigate the computational complexity of maximizing the social welfare and the revenue in these markets, providing hardness and approximation results under various assumptions on the buyers valuations and on the social graph topology.