论文标题
分配鲁棒性：从定价到拍卖
Distributional Robustness: From Pricing to Auctions
论文作者
论文摘要
强大的机制设计是贝叶斯机制设计的替代方法，它产生的设计不依赖于完全分配知识等假设。我们将这种方法应用于销售单个项目的机制，假设仅知道价值分布的平均值和上限的均值。我们寻求一种与与已知参数兼容的最坏情况分布的收入最大化的机制。这样的机制是卖方和选择分布的对手之间零和游戏的平衡，因此可以称为最大最大机制。 Carrasco等。 [2018]当卖方面对该商品的单个投标人时，得出最大最大定价。通过研究两个I.I.D.的规范环境，我们从Max-Min的定价转变为Max-Min拍卖。竞标者并显示最大钟机制是带有随机储备的第二价格拍卖。我们为储备价格以及最糟糕的价值分配提供了封闭式解决方案，并为此提供了简单的经济直觉。实际上，我们为任何数量的投标人提供了封闭式解决方案。 我们解决零和游戏的技术与Carrasco等人的技术大不相同。我们的结果建立了两个竞标者和$ n \ ge 3 $ bidders的情况之间的区别。
Robust mechanism design is a rising alternative to Bayesian mechanism design, which yields designs that do not rely on assumptions like full distributional knowledge. We apply this approach to mechanisms for selling a single item, assuming that only the mean of the value distribution and an upper bound on the bidder values are known. We seek the mechanism that maximizes revenue over the worst-case distribution compatible with the known parameters. Such a mechanism arises as an equilibrium of a zero-sum game between the seller and an adversary who chooses the distribution, and so can be referred to as the max-min mechanism. Carrasco et al. [2018] derive the max-min pricing when the seller faces a single bidder for the item. We go from max-min pricing to max-min auctions by studying the canonical setting of two i.i.d. bidders, and show the max-min mechanism is the second-price auction with a randomized reserve. We derive a closed-form solution for the distribution over reserve prices, as well as the worst-case value distribution, for which there is simple economic intuition. In fact we derive a closed-form solution for the reserve price distribution for any number of bidders. Our technique for solving the zero-sum game is quite different than that of Carrasco et al.- it involves analyzing a discretized version of the setting, then refining the discretization grid and deriving a closed-form solution for the non-discretized, original setting. Our results establish a difference between the case of two bidders and that of $n \ge 3$ bidders.
