[论文解读] Making Auctions Robust to Aftermarkets

Moshe Babaioff, Nicole Immorlica+2 more|arXiv (Cornell University)|Jul 13, 2021

Auction Theory and Applications被引用 2

一句话总结

本文提出了针对具有非监管后市场的多单位市场的鲁棒拍卖设计，表明即使在投机行为下，带有匿名单位保留价的统一定价拍卖或挂牌定价机制，也能在均衡状态下确保至少一半的最优期望福利。核心贡献在于一种福利鲁棒的机制设计，即使在后市场交易存在的情况下也能保持效率，且对现有格式（如碳排放配额拍卖）的改动极小。

ABSTRACT

A prevalent assumption in auction theory is that the auctioneer has full control over the market and that the allocation she dictates is final. In practice, however, agents might be able to resell acquired items in an aftermarket. A prominent example is the market for carbon emission allowances. These allowances are commonly allocated by the government using uniform-price auctions, and firms can typically trade these allowances among themselves in an aftermarket that may not be fully under the auctioneer's control. While the uniform-price auction is approximately efficient in isolation, we show that speculation and resale in aftermarkets might result in a significant welfare loss. Motivated by this issue, we consider three approaches, each ensuring high equilibrium welfare in the combined market. The first approach is to adopt smooth auctions such as discriminatory auctions. This approach is robust to correlated valuations and to participants acquiring information about others' types. However, discriminatory auctions have several downsides, notably that of charging bidders different prices for identical items, resulting in fairness concerns that make the format unpopular. Two other approaches we suggest are either using posted-pricing mechanisms, or using uniform-price auctions with anonymous reserves. We show that when using balanced prices, both these approaches ensure high equilibrium welfare in the combined market. The latter also inherits many of the benefits from uniform-price auctions such as price discovery, and can be introduced with a minor modification to auctions currently in use to sell carbon emission allowances.

研究动机与目标

• 解决主拍卖之后因投机性转售导致的福利损失问题。
• 分析标准拍卖格式（尤其是统一定价拍卖）在与非监管后市场结合时的表现。
• 设计对现有拍卖机制的最小修改，以确保在后市场交易存在的情况下仍能实现高均衡福利。
• 提供理论基础坚实、鲁棒性强的机制，便于实际应用，例如在碳排放配额市场中。

提出的方法

• 引入一个多单位拍卖与后市场相结合的模型，其中投标人可在非监管的二级市场转售物品。
• 提出两种鲁棒机制：带有平衡价格的挂牌定价机制，以及带有匿名单位保留价的统一定价拍卖。
• 使用平衡价格的概念，定义为 p = E[v(OPT(v))]/(2m)，以确保福利保障。
• 应用贝叶斯纳什均衡分析，评估在主拍卖与后市场系统结合下的福利表现。
• 利用价格无序性框架建立福利损失的理论边界。
• 证明了对保留价计算中估计误差的鲁棒性，表明小误差导致的福利损失与误差成比例。

实验结果

研究问题

• RQ1 标准拍卖格式（如统一定价拍卖）在与非监管后市场结合时，能否维持高福利？
• RQ2 对现有拍卖格式进行何种修改，才能在后市场投机行为存在的情况下确保鲁棒的福利保障？
• RQ3 如何设定保留价，以确保在均衡状态下即使在相关估值和信息不对称的情况下，也能实现至少一半的最优期望福利？
• RQ4 福利保障在多大程度上对最优福利估计中的估计误差具有鲁棒性？
• RQ5 对广泛使用的拍卖格式（如统一定价拍卖）进行最小改动（例如增加单位保留价），能否实现鲁棒的效率？

主要发现

• 带有匿名单位保留价 p = E[v(OPT(v))]/(2m) 的统一定价拍卖，在任何贝叶斯纳什均衡下，均能确保至少一半的期望最优福利，无论后市场机制如何。
• 带有平衡价格的挂牌定价机制，在任何后市场和信息结构下，也能在均衡中实现至少一半的期望最优福利。
• 福利保障对估计误差具有鲁棒性：若每单位保留价的误差不超过 ϵ，则福利损失被限制在 mϵ 以内。
• 在对最优福利估计具有高概率置信度的情况下，该机制以至少 1−δ 的概率实现至少 (1−ϵ)/2 的最优期望福利。
• 所提出的保留价机制继承了统一定价拍卖的优点（如价格发现），同时显著提升了对后市场投机行为的鲁棒性。
• 理论上的福利边界是紧致的：即使在单件物品情况下，若无额外假设，近似比也无法优于 1/2。