Equilibria in eBay Auctions

This paper characterizes the set of symmetric Bayesian-Nash equilibria in eBay auctions within the independent private values model. There are multiple equilibria with respect to the bidding time but top two bidders bid their valuations by the end of auction and hence the expected revenue is the same in every equilibrium. EBay auctions are a mixture of traditional ascending and second-price sealed-bid auctions. The eBay auction takes an ascending-bid format but the highest bid is not revealed. A bidder can know every bid except the highest and whether or not he is the highest bidder. The eBay auction ends at the fixed ending time, hence a bidder may not have time to response to his competitior?s bid at the very end of the auction. Therefore, the eBay auction works more like the second-price sealed-bid auction rather than the ascending auction at the end of the auction. In eBay, there are auctions which sell multiple items and/or have a fixed-price component such as "buy-it-now" option. In this paper I focus only on auctions which sell a single item without using a buy-it-now option. While there has beeen a huge literature on empirical analysis of eBay auction data including ?eld experiments, research on equilibria in eBay auctions has been limited. This paper sets up a bidding model for eBay auctions and characterizes all equilibria; this would improve understanding of eBay auction data for empirical work. The rest of the paper is organized as follows: The next section explains the eBay auction format, and Section 3 presents an eBay bidding model and its equilibria with discussion.