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.

翻译：本文研究具有规模不经济的在线$k$选择问题（OSDoS），其中卖方通过为顺序到达的买家优化定价以最大化社会福利，同时考虑递增的边际生产成本。先前研究已探讨此类场景下的确定性动态定价机制。然而，显著挑战依然存在，特别是在小规模或有限库存条件下实现最优性，以及开发有效的随机标价机制。为弥补这一空白，我们针对OSDoS提出一种新颖的随机动态定价机制，相比已有工作提供了更紧的竞争比下界。我们的方法在小库存场景（即$k$较小时）确保最优性能，并在大库存场景（即$k$较大时）超越现有在线机制，从而为不同库存规模下具有规模不经济的在线选择与分配优化问题提供了当前最优的标价机制。