Empirical inference for online auctions

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This dissertation consists of three essays. The first essay adopts the survival analysis to empirically analyze a new auction format, pay-per-bid auction, in which a fee occurs to the bidder when a new bid is submitted. This auction mechanism attracted many theoretical studies and empirical testing in recent years. However, analyzing the pay-per-bid auction under the survival framework provides a novel path to reflect this new auction format as well as involved bidder and seller behaviors. By considering the arrival of bids as a necessary condition for a pay-per-bid auction to survive, survival analysis tools such as Kaplan-Meier (KM) estimate and Accelerated Failure Time (AFT) models are applied to the data set collected from a leading pay-per-bid auction site Swoopo. Cox Proportional Hazard (PH) model is also discussed. Some equilibrium behaviors are confirmed but also some equilibrium deviated behaviors are detected. The second essay models the last-minute bidding behaviors in eBay's hard close auction design using non-parametric analysis. For comparison purpose, the auctions in Amazon with soft close auction design are combined to carry out analysis. The data is selected from eBay and Amazon and a large difference in bid timing is found between auction sites. Density estimation of bid timing confirms the existence of such difference. Mixed additive model is applied to explore the nonparametric relationship between bid timing and parameters of bidding environment. And generalized response model with logistic link function is used to model the probability of a late bidding occurs conditioned on interested covariates. The third essay proposes, from a non-parametric Bayesian aspect, using Dirichlet Processes (DP) with normal mixtures to estimate underlying valuations in second-price ascending auctions under the independent-private-values paradigm. I illustrate how a second-price ascending auction is similar in mechanism to its sealed counterpart and consequently bidders' valuations can be extracted if bidders are identifiable. Compared to classical methods, to provide more flexible and reliable inferences, DP density estimation is strongly motivated and represents an advance. As a non-parametric Bayesian method, DP can accommodate non-nomality through normal mixtures and develop Bayesian inference on model parameters. Due to the complex nature of posteriors, MCMC simulation is used to approximate posteriors as well as density predictions. To test the validity of this method, a Monte Carlo experiment is conducted with similar sample size to our eBay data. In the last section, I reanalyze a data set from eBay auctions and apply our method to estimate the valuations.