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arXiv 2202.09291cs.GT
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贝叶斯和随机时钟拍卖

Bayesian and Randomized Clock Auctions

Michal Feldman, Vasilis Gkatzelis, Nick Gravin, Daniel Schoepflin

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摘要：

在一个单参数机制设计问题中，供应商希望向一组潜在的购买者出售服务。每个购买者$i$具有用于接收服务的私有值$v_i$，并且可行性约束限制可以同时服务哪些购买者集合。最近的经济学研究引入了时钟拍卖作为解决这个问题的高级拍卖，因为它们的透明性，简单性和强激励保证。随后的工作集中在评估这些拍卖的社会福利近似保证，导致强不可能的结果：在没有关于买家价值的先验信息的情况下，没有确定性时钟拍卖可以实现有界近似，即使是简单的可行性约束只有两个最大可行集。我们表明，这些负面结果可以通过使用先验信息或利用随机化来规避。我们提供了时钟拍卖，给出了一般向下封闭的可行性约束$O(\log\log k)$近似与$k$最大可行集为三种不同的信息模型，从完全访问的值分布，完全没有信息。卖家掌握的信息越多，拍卖就越简单。在完全访问下，我们使用一种特别简单的确定性时钟拍卖，称为单一价格时钟拍卖，它只比公布价格机制稍微复杂一点。在这种拍卖中，每个买家提供一个单一的价格，并在那些接受他们的报价的人中选择一个可行的集合。在另一个极端，在没有先验信息的情况下，使用复杂的随机时钟拍卖来获得这种近似保证。除了我们的主要结果，我们提出了一个参数化，插值之间的单一价格的时钟拍卖和一般的时钟拍卖，铺平了道路，一个令人兴奋的未来的研究。

英文摘要：

In a single-parameter mechanism design problem, a provider is looking to sell a service to a group of potential buyers. Each buyer $i$ has a private value $v_i$ for receiving the service and a feasibility constraint restricts which sets of buyers can be served simultaneously. Recent work in economics introduced clock auctions as a superior class of auctions for this problem, due to their transparency, simplicity, and strong incentive guarantees. Subsequent work focused on evaluating the social welfare approximation guarantees of these auctions, leading to strong impossibility results: in the absence of prior information regarding the buyers' values, no deterministic clock auction can achieve a bounded approximation, even for simple feasibility constraints with only two maximal feasible sets. We show that these negative results can be circumvented by using prior information or by leveraging randomization. We provide clock auctions that give a $O(\log\log k)$ approximation for general downward-closed feasibility constraints with $k$ maximal feasible sets for three different information models, ranging from full access to the value distributions to complete absence of information. The more information the seller has, the simpler these auctions are. Under full access, we use a particularly simple deterministic clock auction, called a single-price clock auction, which is only slightly more complex than posted price mechanisms. In this auction, each buyer is offered a single price and a feasible set is selected among those who accept their offers. In the other extreme, where no prior information is available, this approximation guarantee is obtained using a complex randomized clock auction. In addition to our main results, we propose a parameterization that interpolates between single-price clock auctions and general clock auctions, paving the way for an exciting line of future research.

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