arXiv 2105.046972021-05econ.TH

相关鲁棒最优拍卖

Correlation-Robust Optimal Auctions

Wanchang Zhang

摘要：

我研究的拍卖设计中，拍卖人被假定为只有一个通用的投标人的估值的边际分布的信息，但不知道的相关结构的投标人的估值的联合分布。我假设一个通用投标人的估价是有界的，$\bar{v}$是通用投标人的最大估价。在最坏情况下，在与边际分布一致的联合分布的不确定性上评估机制的性能。对于两个投标人的情况下，均匀分布的随机准备金的第二价格拍卖最大化最坏情况下的预期收益在一定的规律性条件下，在所有的优势策略机制。对于$N$-bidder（$N\ge3$）情形，在一定的规则性条件下，第二价格拍卖与$\bar{v}-$缩放的$Beta (\frac{1}{N-1},1)$分布式随机储备最大化了标准（出价不是最高的投标人永远不会被分配）优势策略机制的最坏情况下的期望收益.当概率质量条件（正则性条件的一部分）不成立时，第二价格拍卖与$s^*-$缩放$Beta (\frac{1}{N-1},1)$分布随机储备最大化最坏情况下的预期收益在标准的优势策略机制，其中$s^*\in (0,\bar{v})$。

英文摘要：

I study the design of auctions in which the auctioneer is assumed to have information only about the marginal distribution of a generic bidder's valuation, but does not know the correlation structure of the joint distribution of bidders' valuations. I assume that a generic bidder's valuation is bounded and $\bar{v}$ is the maximum valuation of a generic bidder. The performance of a mechanism is evaluated in the worst case over the uncertainty of joint distributions that are consistent with the marginal distribution. For the two-bidder case, the second-price auction with the uniformly distributed random reserve maximizes the worst-case expected revenue across all dominant-strategy mechanisms under certain regularity conditions. For the $N$-bidder ($N\ge3$) case, the second-price auction with the $\bar{v}-$scaled $Beta (\frac{1}{N-1},1)$ distributed random reserve maximizes the worst-case expected revenue across standard (a bidder whose bid is not the highest will never be allocated) dominant-strategy mechanisms under certain regularity conditions. When the probability mass condition (part of the regularity conditions) does not hold, the second-price auction with the $s^*-$scaled $Beta (\frac{1}{N-1},1)$ distributed random reserve maximizes the worst-case expected revenue across standard dominant-strategy mechanisms, where $s^*\in (0,\bar{v})$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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