Some Evidence on the Winner's Curse: Comment
评论了Thiel（1988）关于拍卖中线性均衡出价策略的论文，指出其方法仅在特殊情况下适用且存在错误，并给出了正确的纳什均衡策略表达式。
The theory of auctions has developed extensively since Robert B. Wilson's (1977) seminal paper. Due to the complexity of equilibrium strategies, however, empirical researchers have been slow to incorporate and test the most basic theoretical precepts.' Typical empirical studies estimate ad hoc bidding models, with no attempt to ascertain whether the implied behaviors are theoretically plausible. The recent paper by Stuart E. Thiel (1988) attempts to bridge this gap. Thiel obtains closed-form equilibrium bidding functions that are theoretically motivated and linear in parameters, and which facilitate empirical estimation and testing. If widely applicable, Thiel's empirical approach would constitute a major methodological breakthrough. Unfortunately, Thiel's approach applies only in special cases that are of limited practical interest. Linear bidding strategies emerge only under circumstances that are unlikely in the real world. The limited range of Thiel's approach may not be apparent to casual readers of his paper. Even when linear strategies do exist, they are not unique under the special assumptions of Thiel's model. For each Nash equilibrium in linear strategies, there exists a related family of nonlinear strategies. Thus, further justification must be found for basing empirical research on the linear specification. We also note a significant error in Thiel's work. The symmetric strategies he derives on the basis of order statistics do not constitute a Nash equilibrium. We derive proper expressions for the symmetric Nash strategies and discuss a specification error in Thiel's regression analysis that would account for the mixed results obtained in his application to the highway-construction industry.