This paper proposes an approach to proving nonparametric identification for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the only available data pertain to the winner's identity and the transaction price. My proof of identification is constructive and is based on establishing the existence and uniqueness of a solution to the system of nonlinear differential equations that describes relationships between unknown distribution functions and observable functions. The proof is conducted in two logical steps. First, I prove the existence and uniqueness of a local solution. Then I describe a method that extends this local solution to the whole support.ududThis paper delivers other interesting results. I demonstrate how this approach can be applied to obtain identification in auctions with a stochastic number of bidders. Furthermore, I show that my results can be extended to generalized competing risks models.
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机译：本文提出了一种在非对称二级价格拍卖中证明投标人价值分布的非参数辨识方法。我考虑的情况是，投标人具有独立的私有价值，并且唯一可用的数据与中标者的身份和交易价格有关。我的身份证明是有建设性的，并且是建立在描述非线性分布方程和可观察函数之间关系的非线性微分方程系统的解的存在性和唯一性的基础上的。证明分两个逻辑步骤进行。首先，我证明了本地解决方案的存在和唯一性。然后，我描述了一种将本地解决方案扩展到整个支持范围的方法。 ud ud本文提供了其他有趣的结果。我演示了如何使用这种方法在具有随机数量投标人的拍卖中获得标识。此外，我证明了我的结果可以扩展到广义竞争风险模型。
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