Envy-Free Pricing in Large Markets: Approximating Revenue and Welfare

We study the classic setting of envy-free pricing, in which a single seller chooses prices for its many items, with the goal of maximizing revenue once the items are allocated. Despite the large body of work addressing such settings, most versions of this problem have resisted good approximation factors for maximizing revenue; this is true even for the classic unit-demand case. In this paper, we study envy-free pricing with unit-demand buyers, but unlike previous work we focus on large markets: ones in which the demand of each buyer is infinitesimally small compared to the size of the overall market. We assume that the buyer valuations for the items they desire have a nice (although reasonable) structure, i.e., that the aggregate buyer demand has a monotone hazard rate and that the values of every buyer type come from the same support.

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