[论文解读] Pricing for online resource allocation: intervals and paths

Shuchi Chawla, J. Benjamin Miller+1 more|arXiv (Cornell University)|Jan 6, 2019

Auction Theory and Applications被引用 14

一句话总结

本文提出了针对具有区间偏好和路径偏好在线资源分配的静态匿名捆绑定价机制，分别实现了次对数级和近乎对数级的竞争比，相较于单品定价实现了指数级的改进。该方法在存在互补性的场景中优化社会福利，其性能随物品供应量线性提升。

ABSTRACT

We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the bundles are drawn from known distributions. This problem is closely related to the so-called prophet-inequality of Krengel and Sucheston [23] and its extensions in recent literature. Motivated by applications to cloud economics, we consider two kinds of buyer preferences. In the first, items correspond to different units of time at which a resource is available; the items are arranged in a total order and buyers desire intervals of items. The second corresponds to bandwidth allocation over a tree network; the items are edges in the network and buyers desire paths.Because buyers' preferences have complementarities in the settings we consider, recent constant-factor approximations via item prices do not apply, and indeed strong negative results are known. We develop static, anonymous bundle pricing mechanisms.For the interval preferences setting, we show that static, anonymous bundle pricings achieve a sublogarithmic competitive ratio, which is optimal (within constant factors) over the class of all online allocation algorithms, truthful or not. For the path preferences setting, we obtain a nearly-tight logarithmic competitive ratio. Both of these results exhibit an exponential improvement over item pricings for these settings. Our results extend to settings where the seller has multiple copies of each item, with the competitive ratio decreasing linearly with supply. Such a gradual tradeoff between supply and the competitive ratio for welfare was previously known only for the single item prophet inequality.

研究动机与目标

• 设计高效的在线资源分配定价机制，适用于买家在物品捆绑中存在互补性的场景。
• 解决传统单品定价因互补性而失效的场景，例如时间区间和树状网络路径分配。
• 在已知买家价值分布的在线设置下，使用静态、匿名的捆绑定价，实现对社会福利的紧密近似。
• 将供应量与竞争比之间的权衡关系从单件预言机不等式扩展至更广泛场景。

提出的方法

• 为在线资源分配中的区间和路径偏好设计静态、匿名的捆绑定价机制。
• 将买家偏好建模为时间有序物品的区间或树状网络中的路径，其价值来自已知分布。
• 使用竞争比分析评估在线买家到达情况下的福利近似保证。
• 证明捆绑定价在区间偏好下实现次对数级竞争比，在路径偏好下实现近乎对数级竞争比，优于单品定价。
• 分析多份物品副本对竞争比的影响，表明竞争比随供应量线性提升。
• 将结果扩展至每种物品存在多个副本的场景，展示供应量与竞争比之间渐进的权衡关系。

实验结果

研究问题

• RQ1 在存在互补性的在线资源分配中，静态、匿名的捆绑定价能否实现优于单品定价的竞争比？
• RQ2 在已知价值分布的在线买家到达场景下，区间偏好下可实现的最优竞争比是多少？
• RQ3 与单品定价相比，捆绑定价在树状网络中的路径偏好下表现如何？
• RQ4 增加物品供应量是否会导致捆绑定价机制的竞争比线性提升？
• RQ5 这些结果能否扩展到每种物品存在多个副本的场景，同时保持紧密的社会福利近似？

主要发现

• 对于区间偏好，静态、匿名的捆绑定价实现了次对数级竞争比，这是在所有在线算法中常数因子范围内的最优结果。
• 对于路径偏好，该机制实现了近乎紧致的对数级竞争比，显著优于单品定价。
• 捆绑定价的竞争比随每种物品可用副本数的增加而线性提升，扩展了单件预言机不等式中已知的权衡关系。
• 在存在互补性的场景中，该结果相较于单品定价实现了指数级改进。
• 这些机制具有真实性，无需动态定价或复杂分配规则，仅依赖于静态、匿名的捆绑价格。
• 该框架适用于实际应用场景，如云资源分配，其中买家请求时间区间或网络路径。