Posted Price Mechanisms for Online Allocation with Diseconomies of Scale

TL;DR

This paper introduces a new randomized posted price mechanism for online allocation with diseconomies of scale, achieving near-optimal performance across small and large inventories, improving upon prior deterministic methods.

Contribution

It proposes a novel randomized dynamic pricing mechanism that provides tighter bounds on competitive ratio and performs optimally for both small and large inventories in OSDoS.

Findings

Achieves tighter lower bounds on competitive ratio.

Ensures optimal performance in small inventory settings.

Surpasses existing mechanisms in large inventory scenarios.

Abstract

This paper addresses the online $k$-selection problem with diseconomies of scale (OSDoS), where a seller seeks to maximize social welfare by optimally pricing items for sequentially arriving buyers, accounting for increasing marginal production costs. Previous studies have investigated deterministic dynamic pricing mechanisms for such settings. However, significant challenges remain, particularly in achieving optimality with small or finite inventories and developing effective randomized posted price mechanisms. To bridge this gap, we propose a novel randomized dynamic pricing mechanism for OSDoS, providing a tighter lower bound on the competitive ratio compared to prior work. Our approach ensures optimal performance in small inventory settings (i.e., when $k$ is small) and surpasses existing online mechanisms in large inventory settings (i.e., when $k$ is large), leading to the best-known posted price mechanism for optimizing online selection and allocation with diseconomies of scale across varying inventory sizes.