Pricing to Maximize Revenue and Welfare Simultaneously in Large Markets

We study large markets with a single seller who can produce many types of goods, and many multi-minded buyers. The seller chooses posted prices for its many items, and the buyers purchase bundles to maximize their utility. For this setting, we consider the following questions: what fraction of the optimum social welfare does a revenue maximizing solution achieve? Are there pricing mechanisms which achieve both good revenue and good welfare simultaneously? To address these questions, we give envy-free pricing schemes which are guaranteed to result in both good revenue and welfare, as long as the buyer valuations for the goods they desire have a nice (although reasonable) structure, e.g., the aggregate buyer demand has a monotone hazard rate or is not too convex. We also show that our pricing schemes have implications for any solution which achieves high revenue: specifically that in many settings, prices that maximize (approximately) profit also result in high social welfare. Our results holds for general multi-minded buyers in large markets with production costs; we also provide improved guarantees for the important special case of unit-demand buyers.