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Elie Tamer for his invaluable help, thoughtful discussions and constant encouragement. I am grateful (2010)
BibTeX
@MISC{Komarova10elietamer,
author = {Tatiana Komarova and To Xiaohong Chen and Emmanuel Guerre and Joel Horowitz and Sokbae Lee and Oliver Linton and Charles Manski and Maria Ponomareva and Xun Tang and Ija Trapeznikova and I Brown},
title = {Elie Tamer for his invaluable help, thoughtful discussions and constant encouragement. I am grateful},
year = {2010}
}
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Abstract
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 identification is con-structive and is based on establishing the existence and uniqueness of a solution to the system of non-linear 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. This paper delivers other interesting results. I show how this approach can be ap-plied to obtain identification in more general auction settings, for instance, in auc-tions with stochastic number of bidders or weaker support conditions. Furthermore, I demonstrate that my results can be extended to generalized competing risks models. Moreover, contrary to results in classical competing risks (Roy model), I show that
Keyphrases
invaluable help elie tamer thoughtful discussion constant encouragement local solution non-linear differential equation support condition roy model observable function stochastic number winner identity risk model unknown distribution function transaction price asymmetric second-price auction nonparametric identification general auction setting independent private value logical step available data pertain interesting result bidder value whole support
