Posted-price mechanisms (PPMs) are a widely adopted strategy for online resource allocation due to their simplicity, intuitive nature, and incentive compatibility. To manage the uncertainty inherent in online settings, PPMs commonly employ dynamically increasing prices. While this adaptive pricing achieves strong performance, it introduces practical challenges: dynamically changing prices can lead to fairness concerns stemming from price discrimination and incur operational costs associated with frequent updates. This paper addresses these issues by investigating posted pricing constrained by a limited, pre-specified number of allowed price changes, denoted by $Δ$. We further extend this framework by incorporating a second critical dimension: risk sensitivity. Instead of evaluating performance based solely on expectation, we utilize a tail-risk objective-specifically, the Conditional Value at Risk (CVaR) of the total social welfare, parameterized by a risk level $δ\in [0, 1]$. We formally introduce a novel problem class kSelection-$(δ,Δ)$ in online adversarial selection and propose a correlated PPM that utilizes a single random seed to correlate posted prices. This correlation scheme is designed to address both the limited price changes and simultaneously enhance the tail performance of the online algorithm. Our subsequent analysis provides performance guarantees under these joint constraints, revealing a clear trade-off between the number of allowed price changes and the algorithm's risk sensitivity. We also establish optimality results for several important special cases of the problem.

翻译：公示定价机制（PPMs）因其简洁性、直观性和激励相容性，已成为在线资源分配中广泛采用的策略。为应对在线环境中固有的不确定性，PPMs通常采用动态递增的定价方式。尽管这种自适应定价能实现较强的性能，但也带来了实际挑战：动态变化的价格可能引发因价格歧视而产生的公平性问题，并因频繁更新而产生运营成本。本文通过研究受限于预先指定的有限允许价格变动次数（记为$Δ$）的公示定价，来应对这些问题。我们进一步扩展该框架，引入第二个关键维度：风险敏感性。我们不再仅基于期望值评估性能，而是采用尾部风险目标——具体而言，即总社会福利的条件风险价值（CVaR），该目标由风险水平$δ\in [0, 1]$参数化。我们正式提出了在线对抗选择中的新问题类别kSelection-$(δ,Δ)$，并提出了一种使用单一随机种子来关联公示价格的相关PPM。该关联方案旨在同时处理有限价格变动问题并提升在线算法的尾部性能。随后的分析在这些联合约束下提供了性能保证，揭示了允许价格变动次数与算法风险敏感性之间明确的权衡关系。我们还针对该问题的若干重要特例建立了最优性结果。