Online Auctions: eBay

1 Introduction
• How to run an auction on the Internet?

• Most important questions:

− What price the highest bidder pays?

− What information is posted about the current bidding?

• One obvious choice is a first-price auction.

− Pay your bid if you win (easy to explain).

− Post highest bid so far.

• But, this makes sense only if

− Bidders logged at the same time and follow in real-time the auction.

− Auction ends when no further bids.

• In practice, people are not watching 24/7 the auction.

− Bidding one’s valuation is not interesting (surplus = 0)

− Makes the game more complicate: how much underbid?

• So, let’s do a second-price auction. But what price should we display?

− Suppose we display the highest bid.

− There are two bids so far: $1 and $100.

− My value is $50: I don’t want to bid (I know I lose).

− Bidder with $100 wins, pays only $1: a disaster for the seller.
• eBay auction format: a mixture of dynamic auction and second-price auction.

− Auctions have a fixed end time (set by the seller).

− The price can last several days or weeks until the end time.

− Potential buyers can bid whenever they want.

− The displayed price is the second-highest bid (+ an increment, discussed later).

− The winner is the highest bidder and pays the price displayed when the auction
ends.
2 eBay: Proxy Bidding

• When placing a bid, eBay asks the maximum bid, and eBay will bid on the
bidder’s behalf, using increments that work like ticking prices:

Current price Bid Increment

$0.01 – $0.99 $0.05
$1.00 – $4.99 $0.25
$5.00 – $24.99 $0.50
$25.00 – $99.99 $1.00
$100.00 – $249.99 $2.50
··· ···
$50, 000.00 and up $100.00
Example 1. The current price on display is $10.00. I bid $30.00. The price goes
to $10.50.

• So, eBay works like a second-price auction:

− eBay bids (on my behalf) “just above” the highest price:

− The previous highest price ($10.00) is in fact now the 2nd highest bid

− The new price is then the 2nd highest bid (+ the $0.50 increment).

• What if there is another bidder comes later and bids $40?

− eBay will automatically compute the outcome of the “bidding war” between me
and the other bidder.

− Up to $30 I continue to bid. At that price I stop (i.e., eBay stops on my behalf).

− The last price is $31, i.e., my final bid of $30 + the increment of $1.
• Since everybody uses the proxy bidding, the auction is solved “immediately”:

− As soon as I bid $30, the price jumps to $31.

− $31 = the lowest bid that the new bidder (with the $40 bid) needs to win.

• Bidders can change their bids and they indeed do so:

− They don’t understand the bidding proxy system.

− They change their estimates of their valuations.

• Bidding several times?

Bidder 1 Bidder 2 Displayed price comment

$1.00 Starting price
$20.00 $1.25 Bidder 1 wins
$40.00 $20.50 Bidder 2 wins
$21.00 $21.50 Bidder 2 wins
$22.00 $22.50 Bidder 2 wins
$23.00 $23.50 Bidder 2 wins
$31.00 $32.00 Bidder 2 wins
$35.00 $36.00 Bidder 2 wins

− Bidder 1 may believe someone is having a bidding war with her.

− If auction deadline is close, bidders can engage in a pursuit by bidding only

small increments, and get more frantic as the deadline approaches.
3 Bid Sniping (Last Minute Bidding)

• Many bidders submit multiple bids in the course of the auction.

• A non-negligible fraction of bids are submitted in closing of the auction, called

“sniping.”

Share of all last bids Share of auctions’ last bids

Last hour 20% 68%
Last 10 minutes 14% 55%
Last 5 minutes 13% 50%
Last 1 minute 8% 37%
Last 10 seconds 2% 12%

− 13% of all bidders submit their bids in the last 5 min

− Half of all auctions have last bids in the last 5 min

3.1 Cost of sniping

• The bid may not be successfully transmitted.

− Buyers complain that their bid was not processed.

− Lower revenue for sellers.

[...] after an auction has closed we receive emails from bidders who claim
they were attempting to place a bid and were unable to get into eBay.
There is nothing we can do to help bidders who were “locked out” while
trying to place a “last minute” bid. (Axis Mundi, a seller in eBay)

• Proxy bidding aimed at protecting bidders against late bidders

− Submitting one’s true valuation is an insurance against snipers.

3.2 Benefits of sniping

• May face inexperienced bidders who bid by small increments:

− If I bid early, then the “incremental bidder” (inexperienced) will overbid and I
may end up with a high price.

− If I bid late, the bid war doesn’t last long ⇒ lower final price

− Last minute bidding: The incremental bidder doesn’t have time to respond. Can
win the auction at the incremental bidder’s low initial bid.

• A kind of implicit collusion of bidders against seller.

− Avoid “bidding war” and suppress some bids.

− Give higher profit to the successful bidders.

• With common values, late bidding has a double rationale:

− More time to gather information from the other bids.

− Avoid giving information to the other bidders.

− Particularly relevant for bidders who are identified as “experts.”

4 Modeling eBay Auctions

• Ockenfels and Roth (2006) provide a model of eBay auctions and analyze strategic
reasons for late bidding.

• There are n bidders. Minimum initial bid m and smallest increment s.

• The “current price” (or “high bid”) in an auction with at least two bidders is
equal to the minimum increment over the second highest bid.

• A player can bid at times t ∈ [0, 1) ∪ {1}.

− A bidder has time to react before the end of the auction to another bidder’s bid
at time t′ < 1.

− At t = 1, everyone knows the bid history prior to t and has time to make exactly
one more bid. The probability that a bid is successfully transmitted is p < 1.
• Private value: Each bidder i has value vi, distributed according to some distribu-
tion F .

• There is no dominant strategy!

− Let n = 2. It is sufficient to show that bidder j with value vj > m + s has no

strategy that is a best response to every strategy of the other bidder i.

− Suppose that bidder i bids m at t = 0 and then does not bid as long as he
remains the high bidder, but bids B(> vj + s) whenever he is not the high
bidder. Bidder j’s best response is not to bid at t < 1 and to bid vj at t = 1.
The payoff to j from this strategy is p(vj − m − s) > 0.

− Suppose that bidder i’s strategy is not to bid at any time. Then, the strategy
for bidder j to bid at t = 1 will give payoff p(vj − m) < vj − m, where the RHS
is the payoff from bidding vj at t = 0.
4.1 Best response to incremental bidding

• Let n = 2. Bidder j is a rational bidder with value vj > m + s, and bidder i an

incremental bidder with value vi > vj + s.

− If bidder j bids vj at t = 1, then the payoff is p(vj − (m + s)).

− If bidder j bids b ≤ vj at some time t < 1, this would be outbid by bidder i at

some t′ ∈ (t, 1) and would raise price above m + s.

− Hence, it is profitable for bidder j to bid vj at t = 1.

4.2 Tacit collusion

• Let n = 2 and both bidders have the same value v, where v > m + 2s.

− Each bidder i does not bid at any time t < 1 and bids v at t = 1.

− If bidder j deviates, i.e., places a bid at t < 1, then bidder i bids v at t′ ∈ (t, 1).

− Equilibrium payoff is p(1 − p)(v − m), while deviation payoff is zero.

− The “threat” of bidding war is credible.

4.3 Protection of information

• The object for sale can be “Fake” with probability pF or “Genuine” with proba-
bility pG = 1 − pF .

• Let n = 2. Bidder U is uninformed and has value vU (F ) = 0 < vU (G) = H.

Bidder I is informed (an expert) with value vI (F ) = 0 < vI (G) = H − c.

− If the object is fake, bidder I wouldn’t place any bid.

− If the object is genuine and bidder I places a bid at some t < 1, then bidder U
can infer that the object is genuine and outbid at some time t′ ∈ (t, 1).

− If the object is genuine and bidder I does not bid before t = 1, then bidder U
wouldn’t bid whenever pG(1 − p)(H − m) − pF m < 0, in which case bidder I
indeed places a bid at t = 1.
5 Amazon versus eBay

• From 1999 to 2006 Amazon had an auction website (like eBay).

• Auctions on Amazon worked very much like eBay:

− English ascending auction, Proxy bidding

− So theoretically it’s a 2nd price auction

• However. . .

− eBay: The auction has a hard deadline

− Amazon: If there’s a bid in the last 10 minutes, the deadline is extended for an
additional 10 minutes.

• Roth and Ockenfels (2002) and Ockenfels and Roth (2006) compare those two.
• Hypothesis about late bidding

Hypothesis Predicted observation

Strategic hypothesis
– Avoid war agains incremental bidders More late
– Implicit collusion bidding on eBay
– Protecting one’s information than Amazon

Non-strategic hypothesis
– Delaying
– Bidders unaware of proxy bidding No difference
– Valuation increases (endowment effect) between Amazon
– Bidders don’t like bids hanging & eBay
5.1 Data analysis

• 480 auctions between Oct. 1999 and Jan. 2000 analyzed.

• Auctions from eBay and Amazon.

• Items: computers & antiques

− Computer: private values, retail prices are easily available, bids convey little
information.

− Antique: interdependent values, retail prices more difficult to obtain, experts

opinion is sometimes required, bids are likely to convey information.
Cumulative distribution of auctions’ last bids
• Experienced bidders bid significantly later on eBay.

− Feedback# reflects the number of transactions a bidder participate in, and thus
the bidders’ experiences.

• For eBay: late bidding significantly more pronounced for antique.

• In a survey, bidders explicitly say that late bidding is

− To avoid bidding wars (and keep the price down).

− To avoid sharing information with other bidders.

6 Summary

• The eBay auction is, at its core, a second-price auction.

− Bidding is made via a proxy: eBay bids on behalf of the bidders.

− eBay auction is dynamic: bidders can update their bids.

− Truthful bidding is not a dominant strategy on eBay.

• Sniping is an important part of eBay auctions.

− Sniping essentially occurs because of hard deadlines.

− Sniping is less likely to occur when valuations are private (as opposed to inter-
dependent or common values).

• The use of auctions on eBay is declining, while the use of posted price increases.
References
Ockenfels, Axel and Alvin E. Roth (2006), “Last-Minute Bidding in Second Price Internet Auctions:
Theory and Evidence Concerning Different Rules for Ending an Action,” Games and Economic
Behavior, 55, 297-320.

Roth, Alvin E. and Axel Ockenfels (2002), “Last-Minute Bidding and the rule for Ending Second-
Price Auctions: Evidence from eBay and Amazon Auctions on the Internet,” American Economic
Review, 92, 1093-1103.