Posted Price Mechanisms for Online Allocation with Diseconomies of Scale

2025-02-04

AI Summary

This paper addresses the online $k$-selection problem with diseconomies of scale (i.e., increasing marginal production costs), aiming to maximize social welfare through dynamic pricing for sequentially arriving buyers. We propose the first randomized posted-price mechanism applicable to arbitrary inventory size $k$, designed by integrating competitive analysis with dynamic pricing theory. Our mechanism achieves the optimal competitive ratio of $1/2$ for unit inventory ($k=1$) and, for large $k$, breaks the performance barrier of existing deterministic mechanisms, attaining the currently best-known lower bound on the competitive ratio—$Omega(1/log k)$—which strictly improves upon all prior deterministic and randomized approaches. To our knowledge, this is the first online posted-price framework that guarantees optimal or near-optimal social welfare across the full range of $k$ under diseconomies of scale.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Maximize social welfare in online selection.
• Address increasing marginal production costs.
• Develop optimal randomized pricing mechanisms.

Innovation

• Randomized dynamic pricing mechanism
• Tighter competitive ratio bound
• Optimal performance across inventory sizes