This paper proposes an approach to proving nonparametric identification for dis-
tributions 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 identifi-
cation is constructive and is based on establishing the existence and uniqueness
of a solution to the system of nonlinear differential equations that describes rela-
tionships 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.
This 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 com-
peting risks models.
Keywords. Second-price auctions, ascending auctions, asymmetric bidders, pri-
vate values, nonparametric identification, competing risks, coherent systems.
JEL classification. C02, C14, C41, C65, D44.