Partial identification in asymmetric auctions in the absence of independence



Summary  This paper examines identification in second-price and ascending auctions within the private-values framework. The first part of the paper considers an arbitrary type of dependence of bidders’ values and analyses identification under several observational scenarios, in which the highest bid is never observed. In a basic scenario, only the winner’s identity and the winning price are observed. The most informative is the scenario in which all the identities and all the bids except for the highest bid are known. Using results from Athey and Haile (2002), the joint distribution of bidders’ values in these scenarios is not identified. The paper uses the information available in auctions’ outcomes to construct bounds on the joint distribution of values for any subset of bidders. The second part of the paper takes a different tack by showing how bounds can be improved under different types of positive dependence of bidders’ values.