Three Essays On All Pay Auctions

The dissertation includes three research papers on all-pay auctions. The first paper (Chapter 1) considers an all-pay auction for a product in which there is an option for bidders to guarantee purchases at a seller specified posted price P at any time. We find the symmetric pure-strategy equilibria in the first- and second-price all-pay auctions (also called war of attrition) with a buy-price option. Under these equilibria the buy-price option will affect high-value bidders' behavior, and improve their welfare. At the same time, the seller can select the optimal posted price to collect more revenue, and the Revenue Equivalence Theorem holds as well. The second paper (Chapter 2) conducts empirical analysis on online penny auctions, which are seen as an adaptation of the famous dollar auction and as "the evil stepchild of game theory and behavioral economics." We use the complete bid and bidder history at a website to study if penny auctions can sustain excessive profits over time. The overwhelming majority of new bidders lose money, but they quit quickly. A very small percentage of bidders are experienced and strategically sophisticated, but they earn substantial profits. Our evidence thus suggests that penny auctions cannot sustain excessive profits without attracting a revolving door of new customers who will lose money. The third paper (Chapter 3) proposes a nonparametric estimation approach to empirical analysis of the war of attrition. In order to construct a tractable model, we consider the uncertain competition and derive a structural model with a stochastic number of bidders. We admit the contamination from observables and introduce a deconvolution problem with heteroscedastic errors into the nonparametric approach. By a two-step nonparametric procedure, we can attain a consistent estimator of the distribution of bidders' private values from the observables. Finally, we apply the estimation procedure to field data from penny auctions.