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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.

We consider a market setting in which buyers are individuals of a population, whose relationships are represented by an underlying social graph. Given buyers valuations for the items being sold, an outcome consists of a pricing of the objects and an allocation of bundles to the buyers. An outcome is social envy-free if no buyer strictly prefers the bundles of her neighbors in the social graph. We focus on the revenue maximization problem in multi-unit markets, in which there are multiple copies of a same item being sold and each buyer is assigned a set of identical items. We consider the four different cases arising by considering different buyers valuations, i.e., single-minded or general, and by adopting different forms of pricing, that is item- or bundle-pricing. For all the above cases we show the hardness of the revenue maximization problem and give corresponding approximation results. All our approximation bounds are optimal or nearly optimal. Moreover, we provide an optimal allocation algorithm for general valuations with item-pricing, under the assumption of social graphs of bounded treewidth. Finally, we determine optimal bounds on the corresponding price of envy-freeness, that is on the worst case ratio between the maximum revenue that can be achieved without envy-freeness constraints, and the one obtainable in case of social relationships. Some of our results close hardness open questions or improve already known ones in the literature concerning the classical setting without sociality.