Shreyas Sekar

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.

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.

Posted Pricing sans Discrimination.

In the quest for market mechanisms that are easy to implement, yet close to optimal, few seem as viable as posted pricing. Despite the growing body of impressive results, the performance of most posted price mechanisms however, rely crucially on price discrimination when multiple copies of a good are available. For the more general case with non-linear production costs on each good, hardly anything is known for general multi-good markets. With this in mind, we study a Bayesian setting where the seller can produce any number of copies of a good but faces convex production costs for the same, and buyers arrive sequentially. Our main contribution is a framework for non-discriminatory pricing in the presence of production costs: the framework yields posted price mechanisms with O(1)-approximation factors for fractionally subadditive (XoS) buyers, logarithmic approximations for subadditive buyers, and also extends to settings where the seller is oblivious to buyer valuations. Our work presents the first known results for Bayesian settings with production costs and is among the few posted price mechanisms that do not charge buyers differently for the same good.

Price Doubling and Item Halving: Robust Revenue Guarantees for Item Pricing

We study approximation algorithms for revenue maximization based on static item pricing, where a seller chooses prices for various goods in the market, and then the buyers purchase utility-maximizing bundles at these given prices. We formulate two somewhat general techniques for designing good pricing algorithms for this setting: Price Doubling and Item Halving. Using these techniques, we unify many of the existing results in the item pricing literature under a common framework, as well as provide several new bicriteria algorithms for approximating both revenue and social welfare simultaneously. The main technical contribution of this paper is a O((log m + log k)2)-approximation algorithm for revenue maximization based on the item halving technique, for settings where buyers have XoS valuations, where m is the number of goods and k is the average supply. Surprisingly, ours is the first known item pricing algorithm with polylogarithmic approximation for such general classes of valuations, and partially resolves an important open question from the algorithmic pricing literature about the existence of item pricing algorithms with logarithmic factors for general valuations