Posted prices vs. negotiations: an asymptotic analysis
Posted prices vs. negotiations: an asymptotic analysis
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公布价格与谈判：渐近分析
DOI：
10.1145/1386790.1386801
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Thomas Holenstein
中科院分区：
文献类型：
--
作者：
Liad Blumrosen;Thomas Holenstein
最佳拍卖的设计着重于与竞标者进行谈判的方法，以获取其持有的相关信息。但是，有时应该很快做出决定，而拍卖师不能允许进行谈判的昂贵迭代程序或等待竞标者确定其确切估值。在实践中使用的一种解决方案是向投标人发布价格，而无需从竞标者那里收集任何信息，并要求他们立即采取意见或付出的响应。
我们的论文比较了全程拍卖中预期的收入与张贴价格拍卖中的预期收入。我们专注于贝叶斯模型中的单项拍卖，在该模型中，投标人愿意为该项目支付的价值是根据已知分布独立分配的。
本文提供了上述每一个拍卖中每一个获得的最佳预期收入的确切渐近表征。对于发布的价格拍卖，我们还提出了实现最佳结果的确切价格。我们的结果被赋予降低渐近顺序的条件，即1 - o（1）。我们提供两组结果；一个用于从上方界限的支持上的分布，而在无界支持上进行的第二组进行分配。在第一种情况下，我们需要对分布函数接近支撑末端的方式的温和假设，称为第一个von Mises条件；后一种情况需要类似的温和条件，称为第二冯·米塞斯条件。这些非常弱的条件取自有关极端价值理论和最高阶段统计的作品。
The design of optimal auctions focuses on ways to negotiate with the bidders for eliciting relevant information that they hold. Sometimes, however, decisions should be made very quickly, and the auctioneer cannot allow a costly iterative procedure of negotiation or waiting for bidders to determine their exact valuation. One solution that has been used in practice is to post prices for the bidders, without collecting any information from the bidders, and ask for their immediate take-it-or-leave-it response.
Our paper compares the expected revenue in full-revelation auctions to that in posted-price auctions. We focus on single-item auctions in a Bayesian model where the values that the bidders are willing to pay for the item are independently identically distributed according to a known distribution.
This paper provides an exact asymptotic characterization of the optimal expected revenue achieved by each one of the above auctions. For posted price auctions, we also present the exact prices that achieve the optimal results.Our results are given up to terms with lower asymptotic order, that is, up to factor of 1--o(1). We provide two sets of results; one for distributions on a support that is bounded from above, and a second set for distributions on unbounded supports. In the first case we require a mild assumption on the way the distribution function approaches the end of the support, called the first von Mises condition; the latter case requires a similar mild condition called the second von Mises condition. These very weak conditions are taken from works on extreme-value theory and highest-order statistics.