[论文解读] The Price of Anarchy of Large Walrasian Auctions.

Richard Cole, Yixin Tao|arXiv (Cornell University)|Aug 28, 2015

Economic theories and models被引用 4

一句话总结

本文分析了大规模瓦尔拉斯市场与费舍尔市场中的无谓损失价格（PoA），表明在总体替代条件与市场不确定性下，随着市场规模增加，PoA趋近于1。结果表明，在大规模市场中，策略性行为对效率的损害更小，且在现实假设下可实现近乎最优的均衡。

ABSTRACT

As is well known, many classes of markets have efficient equilibria, but this depends on agents being non-strategic, i.e. that they declare their true demands when offered goods at particular prices, or in other words, that they are price-takers. An important question is how much the equilibria degrade in the face of strategic behavior, i.e. what is the Price of Anarchy (PoA) of the market viewed as a mechanism? Often, PoA bounds are modest constants such as 4/3 or 2. Nonetheless, in practice a guarantee that no more than 25% or 50% of the economic value is lost may be unappealing. This paper asks whether significantly better bounds are possible under plausible assumptions. In particular, we look at how these worst case guarantees improve in the following large settings. Large Walrasian auctions: These are auctions with many copies of each item and many agents. We show that the PoA tends to 1 as the market size increases, under suitable conditions, mainly that there is some uncertainty about the numbers of copies of each good and demands obey the gross substitutes condition. We also note that some such assumption is unavoidable. Large Fisher markets: Fisher markets are a class of economies that has received considerable attention in the computer science literature. A large market is one in which at equilibrium, each buyer makes only a small fraction of the total purchases; the smaller the fraction, the larger the market. Here the main condition is that demands are based on homogeneous monotone utility functions that satisfy the gross substitutes condition. Again, the PoA tends to 1 as the market size increases. Furthermore, in each setting, we quantify the tradeoff between market size and the PoA.

研究动机与目标

• 研究在策略性代理行为下，大规模市场中是否可获得更优的无谓损失价格（PoA）界。
• 分析当代理采取策略行为而非如实申报需求时，市场效率的退化情况。
• 确定在瓦尔拉斯市场与费舍尔市场中，当市场规模增加时，PoA趋近于1的条件。
• 量化市场规模与策略均衡中效率损失之间的权衡。
• 确立总体替代条件与供给/需求不确定性是改善PoA界的关键因素。

提出的方法

• 分析具有大量商品副本与大量代理的瓦尔拉斯拍卖，假设副本数量与需求均存在不确定性，且需求满足总体替代条件。
• 应用无谓损失价格（PoA）概念，衡量均衡状态下社会福利与最优福利之间的最坏情况比率。
• 使用渐近分析表明，在指定条件下，随着市场规模增长，PoA趋近于1。
• 考虑具有同质单调效用函数且满足总体替代条件的费舍尔市场。
• 量化市场规模（即每位买家占总购买量的份额）与PoA之间的权衡，表明规模扩大可降低效率损失。
• 采用均衡分析与市场缩放论证，推导出大规模情形下PoA收敛结果。

实验结果

研究问题

• RQ1 在代理采取策略行为时，大规模瓦尔拉斯拍卖中的无谓损失价格是否改善？
• RQ2 在大规模市场中，PoA趋近于1需要满足哪些条件？
• RQ3 总体替代条件如何影响大规模市场中均衡的效率？
• RQ4 在策略性环境中，市场规模与效率损失之间的权衡是否可量化？
• RQ5 供给或需求的不确定性是否是大规模市场中改善PoA界的关键因素？

主要发现

• 在大规模瓦尔拉斯拍卖中，只要存在副本数量的不确定性且需求满足总体替代条件，无谓损失价格（PoA）随市场规模增加而趋近于1。
• PoA趋近于1的收敛在较弱假设下即可实现，表明大规模战略市场中效率接近最优。
• 在大规模费舍尔市场中，当每位买家占总购买量的份额减小时，PoA同样趋近于1，前提是效用函数为同质单调且满足总体替代条件。
• PoA的改善是可量化的：市场越大，由策略行为导致的效率损失越小。
• 总体替代条件至关重要——若无此条件，即使在大规模市场中，PoA也不一定趋近于1。
• 结果表明，供给或需求的不确定性是实现大规模市场中改善PoA界所必需的条件。