Online Posted Pricing with Unknown Time-Discounted Valuations

TL;DR

This paper develops and analyzes posted-price mechanisms for selling a single item over time with unknown, discounted customer valuations, providing optimal strategies and empirical validation for different valuation scenarios.

Contribution

It introduces new mechanisms for online posted pricing under unknown, discounted valuations, including optimal and practical strategies with theoretical guarantees.

Findings

Mechanism M_c achieves optimal competitive ratio in identical valuation setting.

Mechanism M_pc performs well with limited price adjustments.

Empirical results validate the effectiveness of proposed mechanisms.

Abstract

We study the problem of designing posted-price mechanisms in order to sell a single unit of a single item within a finite period of time. Motivated by real-world problems, such as, e.g., long-term rental of rooms and apartments, we assume that customers arrive online according to a Poisson process, and their valuations are drawn from an unknown distribution and discounted over time. We evaluate our mechanisms in terms of competitive ratio, measuring the worst-case ratio between their revenue and that of an optimal mechanism that knows the distribution of valuations. First, we focus on the identical valuation setting, where all the customers value the item for the same amount. In this setting, we provide a mechanism M_c that achieves the best possible competitive ratio, discussing its dependency on the parameters in the case of linear discount. Then, we switch to the random valuation setting. We show that, if we restrict the attention to distributions of valuations with a monotone hazard rate, then the competitive ratio of M_c is lower bounded by a strictly positive constant that does not depend on the distribution. Moreover, we provide another mechanism, called M_pc, which is defined by a piecewise constant pricing strategy and reaches performances comparable to those obtained with M_c. This mechanism is useful when the seller cannot change the posted price too often. Finally, we empirically evaluate the performances of our mechanisms in a number of experimental settings.