The ebay market as sequential second price auctions: Theory and experiments,” November 2006, unpulbished manuscript. 22

We consider the sequential second price auction in which the two highest bids are an-nounced after each stage with unit demand bidders of affiliated private values. We find an efficient symmetric sequential equilibrium in monotonic strategies where bidders bid the ex-pected winning price of the next stage, conditional on being the tied winner in this stage. Such an equilibrium survives in an eBay auction setting, in which bidders are allowed to submit mul-tiple proxy (second-price) bids in a given fixed time period, when all bidders bid only at the last minute, or snipe. We then conduct controlled (laboratory) experiments with the special case of three items sold to bidders with independent private values, using either a sealed-bid second price auction or an eBay auction format. We show the timing of bidding in the eBay auction demonstrate “last minute bidding (sniping) ” as reported by Roth and Ockenfels (2002), and early “squatting ” coined by Ely and Hossain (2006). Moreover, both formats achieve high ef-ficiency levels and have estimated bid functions seemly as predicted. However, prices decline, but revenue is higher than predicted in the early stages. Individual bids reveal that a significant portion of subjects either bid their valuations or zero in early auctions, even though they bid their valuations in the last one. To explain this, we construct a steps-of-thinking (cognitive hierarchy) model anchored on L0 bidders who always bid their valuations. The combination of various types of bidders explain the data better than that of standard equilibrium theory and shed light on the “declining price anomaly ” documented by Ashenfelter (1989) and previously attributed to extreme risk aversion by McAfee and Vincent (1993)