Static Pricing for Online Selection Problem and its Variants

TL;DR

This paper demonstrates that simple static pricing algorithms can achieve near-optimal guarantees in adversarial online selection problems, including variants like online assignment and convex cost scenarios.

Contribution

It introduces optimal static pricing algorithms for adversarial online selection and its variants, matching the best dynamic algorithms' competitive ratios.

Findings

Static pricing algorithms achieve strong guarantees comparable to dynamic algorithms.

Optimal static pricing algorithms are designed for online selection, assignment, and convex cost variants.

Proposed approaches include an economics-based analysis and a novel representative function method.

Abstract

This paper studies an online selection problem, where a seller seeks to sequentially sell multiple copies of an item to arriving buyers. We consider an adversarial setting, making no modeling assumptions about buyers' valuations for the items except acknowledging a finite support. In this paper, we focus on a class of static pricing algorithms that sample a price from a pre-determined distribution and sell items to buyers whose valuations exceed the sampled price. Such algorithms are of practical interests due to their advantageous properties, such as ease of implementation and non-discrimination over prices. Our work shows that the simple static pricing strategy can achieve strong guarantees comparable to the best known dynamic pricing algorithms. Particularly, we design the optimal static pricing algorithms for the adversarial online selection problem and its two important variants: the online assignment problem and the online selection with convex cost. The static pricing algorithms can even attain the optimal competitive ratios among all online algorithms for the online selection problem and the online assignment problem. To achieve these results, we propose an economics-based approach in the competitive analysis of static pricing algorithms, and develop a novel representative function-based approach to derive the lower bounds. We expect these approaches will be useful in related problems such as online matching.