THE OPTIMAL LISTING STRATEGIES IN ONLINE AUCTIONS

• Date: 01 May 2017
• Author: Kong‐Pin Chen,Chi‐Hsiang Liu,Chien‐Ming Wang,Szu‐Hsien Ho
• DOI: http://doi.org/10.1111/iere.12222
• Published date: 01 May 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 2, May 2017

THE OPTIMAL LISTING STRATEGIES IN ONLINE AUCTIONS∗

BYKONG-PIN CHEN,SZU-HSIEN HO,CHI-HSIANG LIU,AND CHIEN-MING WANG1

Academia Sinica, Taiwan; National Taiwan University,Taiwan; Hubei University of Economics,

China; Hubei University of Economics, China

This article proposes a unified framework to completely characterize the seller’s optimal listing strategy in

the online auction as a function of her rate of time impatience. Specifically, the fixed-price listing, the regular

auction, and the buy-it-now (BIN) auction are each a solution of the seller’s single optimization problem under

different values of the rate of intertemporal discount: The perfectly patient seller adopts the regular auction,

the sellers with a medium range of time impatience adopt the BIN auction, and the most impatient of sellers

adopt the fixed-price listing. Moreover, under mild conditions, the reverse price is inversely related to the value

of the seller’s discount factor, either within or across formats. This in turn implies that the posted price in the

fixed-price sale is greater than the reserve price of the BIN auction, followed by that of the regular auction.

These predictions offer clear empirical implications.

1. INTRODUCTION

Although the Revenue Equivalence Theorem has identified a very general condition under

which all auction formats yield exactly the same expected revenue to the seller, in reality the

sellers have many other considerations than expected revenue itself. In the online auctions,

their considerations are even more diverse. This is because the online auction offers the sellers

a variety of formats to list their items, which affect other dimensions of the auction’s outcomes

than revenue. One important consideration, which is the main concern of this article, is that

unlike the traditional virtual auctions whose bidding process rarely takes more than one hour,

the duration of an online auction generally lasts for several days. Therefore, transaction rules

that help to satisfy the seller’s or the buyer’s time preference are important.

Depending on the difference in the bidding rules, there are three major listing formats in the

online auctions. The first is the usual ascending price auction. The seller lists an item by posting

a fixed bidding duration (hereafter called “posted duration”), either with or without a reserve

price.2The highest bidder at the end of the posted duration is the winner. To clearly distinguish

between auctions of different formats, in this article we will call it the “regular auction.” Since

most auction sites adopt the proxy bid rule, the online regular auction is essentially a second-

price auction, and almost all the literature treats the online regular auctions as such. The second

format is the fixed-price listing: An item is listed for a specific posted duration with a fixed posted

price, and the bidder who is willing to pay this price can place an order at any time within the

posted duration to win the item. The third format, which is a specific online auction innovation,

is the buy-it-now (BIN) auction. On top of the regular auction, the seller sets a price, called the

BIN price, under which the bidder has the additional option to win the item immediately by

∗Manuscript received September 2014; revised February 2016.

1We sincerely thank the editor, Holger Sieg, and three referees for very useful comments and suggestions. The

first author’s research is supported by a grant from Taiwan’s Ministry of Science and Technology (#103-2410-H-001-

006-MY3). Please address correspondence to: Kong-Pin Chen, Research Center of Humanities and Social Sciences,

Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei 11529, Taiwan. E-mail: kongpin@gate.sinica.edu.tw.

2In the online auction, there are two types of reserve price. The publicly observed reserve price is in the form of the

starting (minimum) bid. The first bid must be at least as high as the starting bid to be eligible. Another type of reserve

price, the secret reserve price, is one set by the seller that cannot be publicly observed. A bidder who bids below the

secret reserve price will only be informed as such, without learning its value.

421

C

(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

422 CHEN ET AL.

agreeing to pay that price any time within the posted duration. In the eBay auction (which is

the main concern in this article), the BIN option is temporary: If a bidder places a bid before

any other bidder exercises BIN, then the BIN option disappears, and the BIN auction reduces

to a regular auction.3Hasker and Sickles (2010) have shown in their eBay auction data that all

three formats occupy significant portions among all listings.4

An obvious question to ask is: What determines a seller’s choice of one format over the

others? There is surprisingly little research that addresses this question. In a seminal paper,

Wang (1993) compared the fixed-price sale and the regular auction. He showed that, if bidders’

valuations are independent and they arrive randomly, the regular auction will be the more

preferable to the seller relative to fixed-price sale, the steeper the buyer’s marginal-revenue

curve. His model compares only the regular auction and the fixed-price sale.

Wang et al. (2008) assume that bidders have different costs of participating in a regular

auction and a BIN auction. Depending on the relative cost, there exists a threshold value of the

bidder’s valuation above which he prefers exercising BIN to bidding. This in turns characterizes

two cutoff values, one high and one low. If the BIN price is set to be higher than the high cutoff,

no bidder will exercise BIN, and the BIN auction is essentially a regular auction. If the BIN

price is set lower than the low cutoff, then all bidders prefer to exercise BIN instead of bidding,

and the BIN auction is essentially a fixed-price posting. Only if the BIN price is set between

the two cutoff values is the auction a true BIN auction. This model, however, implies that the

fixed-price auction will result in the lowest price among all formats, essentially because its BIN

price is so low that every bidder wants to exercise it. This not only is at odds with intuition,

but is also inconsistent with the extant empirical literature, which consistently shows that the

transaction price of the fixed-price listing is the highest among all formats (Hammond, 2010;

Einav et al., 2013).5

In this article, we propose a simple theory to capture the sellers’ strategic consideration

in selecting the listing formats as a function of their time preferences. The difference in the

bidding rules for the three formats discussed above has strong implication for the expected

length of time needed for completion of a transaction (hereafter called the “sale duration”)

in each format. This in turn provides the intuition on how each format can serve the needs of

sellers with different time preferences. The regular auction needs to run the whole length of its

posted duration to determine the highest bidder as winner. On the other hand, in a fixed-price

listing, the transaction is completed as soon as the first bidder places an order. The BIN auction

lies in between: If some bidder exercises BIN first, transaction will be completed immediately.

If, however, some bidder places a bid first, then the BIN auction reduces to a regular auction,

and will then run until the end of the posted duration to complete the transaction. This implies

that, given identical posted duration, the regular auction will take the longest expected length

of time to complete the transaction, followed by the BIN auction, with the fixed-price listing

the shortest. Given that regular auction (with reserve price) is the optimal auction in terms of

revenue (Myerson, 1981), the choice of the three formats is to balance the trade-off between

revenue and payoff delay.

3eBay has changed the rule for BIN frequently. At the time the article was written, BIN disappears in the motors

category only if the bid is greater than starting bid by a certain amount. In other categories, BIN disappears as soon

as some bidder places a bid. Currently, in some categories (Parts and Accessories of the eBay Motors) the BIN option

disappears when the price rises to 30% of the starting price. In some other categories (Cell Phones and Accessories;

Clothing, Shoes, and Accessories; and Tickets), the BIN option disappears when the price rises to 50%. For the other

categories, the BIN option disappears as soon as someone bids. Please see http://pages.ebay.com/help/buy/how-buy-

bin.html. We thank a referee for pointing this out to us.

4Einav et al. (2013), however, had shown that the proportion of regulation auction (fixed-price listings) has substan-

tially decreased (increased) in the past decade.

5Also, in the model of Wang et al. (2008), sellers’ choice of format is not based on their own characteristics, but

on their perception of the bidders’ valuations. This implies that the sellers adopt different formats because of their

difference in perceptions, which also implies that some sellers’ perceptions are incorrect. In a word, their model is not

an equilibrium model.