Pricing to Maximize Revenue and Welfare Simultaneously in Large Markets

TL;DR

This paper develops efficient pricing schemes in large markets that simultaneously maximize revenue and social welfare, especially when buyer valuations have certain structured properties, improving outcomes for sellers and buyers.

Contribution

It introduces new pricing mechanisms that guarantee both high revenue and welfare in large markets with multi-minded buyers under structured valuation assumptions.

Findings

Pricing schemes achieve good revenue and welfare when buyer demand has a monotone hazard rate.

Schemes ensure high social welfare without sacrificing profit for revenue-focused sellers.

Improved guarantees for unit-demand buyers in large markets.

Abstract

We study large markets with a single seller which 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 efficient 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., that 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 pricing which achieves high revenue: specifically that even if the seller cares only about revenue, they can still ensure that their prices result in good social welfare without sacrificing profit. Our results holds for general multi-minded buyers in large markets; we also provide improved guarantees for the important special case of unit-demand buyers.