[论文解读] From Bayesian to Crowdsourced Bayesian Auctions.

Jing Chen, Bo Li+1 more|arXiv (Cornell University)|Feb 5, 2017

Auction Theory and Applications参考文献 48被引用 3

一句话总结

本文提出众包贝叶斯拍卖，通过将投标人价值分布的知识分散在各方和卖家之间，放宽了常见的先验假设。它为单位需求和可加性拍卖设计了两步主导策略机制，随着知识的增加，实现的收益接近最优贝叶斯机制的100%，表明当知识被众包时，常见先验假设在收益方面几乎无损失。

ABSTRACT

A strong assumption in Bayesian mechanism design is that the distributions of the players' private types are common knowledge to the designer and the players--the common prior assumption. An important problem that has received a lot of attention in both economics and computer science is to repeatedly weaken this assumption in game theory--the Wilson's Doctrine. In this work we consider, for the first time in the literature, multi-item auctions where the knowledge about the players' value distributions is scattered among the players and the seller. Each one of them privately knows some or none of the value distributions, no constraint is imposed on who knows which distributions, and the seller does not know who knows what. In such an unstructured information setting, we design mechanisms for unit-demand and additive auctions, whose expected revenue approximates that of the optimal Bayesian mechanisms by crowdsourcing the players' and the seller's knowledge. Our mechanisms are 2-step dominant-strategy truthful and the revenue increases gracefully with the amount of knowledge the players have. In particular, the revenue starts from a constant fraction of the revenue of the best known dominant-strategy truthful Bayesian mechanisms, and approaches 100 percent of the later when the amount of knowledge increases. Our results greatly improve the literature on the relationship between the amount of knowledge in the system and what mechanism design can achieve. In some sense, our results show that the common prior assumption is without much loss of generality in Bayesian auctions if one is willing to give up a fraction of the revenue.

研究动机与目标

• 为解决贝叶斯机制设计中的强常见先验假设，即所有参与者必须知晓他人价值分布的先验。
• 建模一种现实场景，其中关于价值分布的知识是无结构且分散在投标人和卖家之间的。
• 设计利用这种分布式知识来近似最优贝叶斯机制收益的诚实机制。
• 量化随着分布式知识量的增加，收益如何提升，表明收益平滑趋近最优收益。

提出的方法

• 设计一种两步机制，投标人报告其对价值分布的私有知识，卖家利用这些信息计算分配和支付。
• 通过确保无论他人行为如何，诚实报告知识始终是最优策略，实现主导策略诚实性。
• 使用贝叶斯最优机制作为基准，并在不同水平的分布式知识下与之比较收益。
• 应用收益近似框架，将机制性能相对于最优贝叶斯机制进行边界约束。
• 引入一种知识聚合协议，将投标人和卖家提供的部分先验信息整合，形成对价值分布的全局估计。
• 从收益近似角度分析机制性能，表明其随分布式知识总量的增加而单调提升。

实验结果

研究问题

• RQ1 当常见先验假设被违反且知识分散在投标人和卖家之间时，如何扩展贝叶斯机制设计？
• RQ2 在仅掌握价值分布部分知识的情况下，多物品拍卖中的收益能被近似到何种程度？
• RQ3 能否在此类无结构知识环境下设计出诚实机制，同时仍实现高收益？
• RQ4 所提机制的收益如何随分布式知识总量的变化而变化？
• RQ5 常见先验假设对于高收益机制是否必要，还是可在最小收益损失下被放宽？

主要发现

• 所提机制具有主导策略诚实性，确保所有参与者诚实报告知识始终是最优策略。
• 当可用知识较少时，机制的收益即达到最优贝叶斯机制收益的一个常数比例。
• 随着分布式知识总量的增加，机制的收益趋近于最优贝叶斯机制收益的100%。
• 收益随知识量的增加单调且平滑提升，表明信息可得性与性能之间存在平稳的权衡。
• 结果表明，若允许付出少量收益损失以换取更低的知识要求，则常见先验假设带来的收益损失可忽略不计。