Posted Pricing sans Discrimination

TL;DR

This paper develops non-discriminatory posted pricing mechanisms for multi-good markets with convex production costs, achieving near-optimal revenue approximations in Bayesian settings with various buyer valuation classes.

Contribution

It introduces a novel framework for non-discriminatory posted prices in markets with production costs, providing the first known Bayesian results in this setting.

Findings

O(1)-approximation for XoS buyers

Logarithmic approximation for subadditive buyers

Extends to oblivious seller valuation scenarios

Abstract

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.