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.
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