Auctions with Buy Prices

Abstract

The major internet auction sites eBay and Yahoo have developed innovative hybrid auction designs that incorporate buy prices. My dissertation focuses on the Buy It Now (BIN, hereafter) version of the auctions on eBay, the largest online auction site. The BIN hybrid auction combines a standard ascending bid auction with a posted-price offer. A seller in a BIN auction lists his auction with a "buy price". A bidder may purchase the item immediately at the buy price and end the auction. If he places a bid instead, the option to purchase the item at the buy price disappears and the subsequent bidders participate in the standard eBay auction. This auction format has been very popular with both buyers and sellers. In 2005 eBay's sales in fixed price platform (BIN and Half.com) totaled $13.8 billion, which was 33.1% of eBay's total sales.The dissertation explores the BIN auctions using theory, experiments and field data. Chapter 1 theoretically analyzes BIN auctions within the common values framework. An equilibrium is characterized, shown to exist, and the revenues generated by BIN and standard eBay auctions are compared. Chapter 2 compares the bidding behavior and the revenue implications of BIN auctions in lab experiments under common and private value assumptions. The third develops an "incomplete" theoretical model of BIN auctions within the private values framework. An "incomplete" empirical specification is derived and then field data collected from eBay's BIN auctions are used to estimate the primitives of the model, including the bidders' risk aversion and time preference. I then explore how heterogeneity of sellers and items influence these primitives. Chapter 1 (Common Values Auctions with a Buy Price: the case of eBay): Several explanations for the popularity of buy price have been provided for independent private value auctions. Risk aversion and impatience of either the bidders or the seller have mainly been used to explain the popularity of buy prices in IPV models. This paper, using a pure common value framework, models auctions with eBay-style "temporary" buy prices, when the bidders and the seller are either risk neutral or risk averse. It characterizes equilibrium bidding strategies in a general setup and then analyzes a seller's incentive to post a buy price when there are two bidders. When bidders are either risk neutral or risk averse there is no incentive to post a buy price for a risk neutral seller. But when the seller is risk averse, a suitably chosen buy price can raise the seller's expected utility when the bidders are either risk neutral or risk averse. Chapter 2 (An Experimental Study of Auctions with a Buy Price Under Private and Common Values): We use experiments to examine several predictions from the theoretical studies of buy prices. The theoretical predictions from Wooders and Reynolds (2003) and Chapter 1 show that the introduction of a buy price causes the seller's revenue to move in opposite directions in private value and common value settings. Meanwhile, Mathews and Katzman (2006) find that risk averse sellers might find buy prices advantageous because they reduce the variance in seller revenue in eBay auctions with risk-neutral bidders. The lab experiments are used to answer three key questions. (a) Can a buy price raise seller revenue and lower the variance of seller revenue in an independent private value auction? (b) Does a buy price lower seller revenue in common value auctions? (c) If the theoretical predictions do not hold, can a behavioral model explain the patterns observed in the data? Using a between-subjects design the results show that the use of a buy price has a positive and statistically significant effect on seller revenue in private value auctions. The buyers are risk averse. The estimate of the Constant Absolute Risk Aversion (CARA) index of 1.11 for the bidders is equivalent to a Constant Relative Risk Aversion (CRRA) index of 0.62 which is centered within the range of other estimates of relative risk aversion. As predicted by the theory when buyers are risk averse, the use of a buy price yields a statistically significant reduction in the variance of seller revenue. Hence, as predicted, the use of a buy price is advantageous to the seller when either the bidders or the seller are risk averse. The results for common value auctions are inconsistent with the theoretical predictions. Use of a buy price did not lower seller revenue, and the bidders' behavior departed from theoretical predictions in several respects. As a result, we develop and estimate a behavioral model of common value BIN auctions based on the winner's curse and overweighting of a bidder's private information. We find statistically significant evidence of overweighting of the bidder's own signal and estimated a CARA index of 0.001. This behavioral model explains all the departures from the rational model we found in the common values experiments. Chapter 3 (The Buy-it-now Option, Risk Aversion, and Impatience in an Empirical Model of eBay Bidding): Haile and Tamer (2003) first used an incomplete econometric model in an auction context, assuming that bidders bid up to their values and do not allow an opponent to win at a price they are willing to beat. Canals-Cerda and Pearcy (2004) used a similar incomplete econometric model to study eBay auctions while adding the assumption that the maximum of all the bids placed by the bidder with the second highest value is exactly equal to his value. Chapter 3 extends these incomplete models to eBay's BIN auctions. We develop and estimate an equilibrium model for BIN independent private value auctions with a stochastic and unknown number of potential bidders who enter the auction sequentially. In the model risk averse and time impatient bidders buy at the BIN price because it allows them to avoid the uncertainties and delay of the ascending bid auction that takes place if no one chooses the BIN option. As a result, the bidders' decisions to choose the BIN option in BIN auctions of different lengths can be used to identify the bidders' risk aversion and time preference parameters. Our model is "incomplete" in the sense that we do not impose any stylized structure on bidding in the ascending bid auction and, although bid revision is allowed, the process is not explicitly described. Our "incomplete" econometric model uses a partial likelihood approach proposed by Cox (1975) that allows the analysis to bypass modeling bidding and the bid revision process. The model is estimated using a new data set of 3245 eBay auctions of Pentium-3 laptops that ran between 22 July to 10 August 2005.