Bayesian Inference in Structural Second-Price Auctions with both Private-Value and Common-Value Bidders
(English)Manuscript (preprint) (Other academic)
Auctions with asymmetric bidders have been actively studied in recent years. Tan and Xing (2011) show the existence of monotone pure-strategy equilibrium in auctions with both private-value and common-value bidders. The equilibrium bid function is given as the solution to an ordinary differential equation (ODE). We approximate the ODE and obtain a very accurate, approximate inverse bid as an explicit function of a given bid. This results in fast and numerically stable likelihood evaluations, which is an extremely valuable property for inference. We propose a model where the valuations of both common-value and private-value bidders are functions of covariates. The probability of being a common-value bidder is modeled by a logistic regression model with Bayesian variable selection. The model is estimated on a dataset of eBay coin auctions. We analyze the model using Bayesian methods implemented via a Metropolis-within-Gibbs algorithm. The posterior inference of the common-value part of the model is similar to the ones obtained from a model with only common-value bidders, whereas the private-value part of the model is more affected by the introduction of common-value bidders. There is on average a slightly larger probability for a bidder to be a common-value bidder, but this probability depends very little on the auction-specific covariates.
Probability Theory and Statistics
Research subject Statistics
IdentifiersURN: urn:nbn:se:su:diva-57276OAI: oai:DiVA.org:su-57276DiVA: diva2:415132