An endowment effect can result in both multiple bidding and sniping in auctions. It can cause players to bid multiple times and overpay for items. Sniping is a rational response for experienced bidders looking to avoid the endowment effect.auction, eBay, multiple bidding, sniping, endowment effect

Christopher Cotton

English

Research Papers in Economics

Sniping to Avoid the Endowment Eect in Auctions
Christopher Cotton
September 2009
Abstract
An endowment eect can result in both multiple bidding and sniping in auctions. It can
cause players to bid multiple times and overpay for items. Sniping is a rational response for
experienced bidders looking to avoid the endowment eect.
JEL: D44, D83
Keywords: auction, eBay, multiple bidding, sniping, endowment eect
Introduction
In online auctions on eBay and Amazon.com, some bidders increase their bids over the course of an
auction (commonly called multiple bidding), others wait until the closing moments of an auction
to bid (commonly called sniping) (Roth and Ockenfels 2002, Ariely et al. 2005). Such behavior is
inconsistent with standard auction models.
This paper formally incorporates a simple model of an \endowment eect" into a private-value,
second-price auction and shows how it leads to both multiple bidding and sniping. The term
endowment eect describes the tendency of people to value a good more when they think of it as
their own (Thaler 1980). In an auction, this means that a player's willingness to pay for an item
depends on whether he expects to win the auction (Heyman et al. 2004).1 Although other papers
suggest that the endowment eect causes multiple bidding, we are the rst to show it may also
cause sniping.2
It is relatively straightforward to see how the endowment eect may result in multiple bidding.
the endowment eect may cause an early bidder to increase his valuation. He may then increase
his bid (thus engaging in multiple bidding).
Department of Economics, University of Miami, Coral Gables, FL 33146; cotton@miami.edu.
1The endowment eect has been widely documented in the literature (e.g., Kahneman et al. 1990). We use the
term endowment eect to refer to the eect both when ownership is rmly established and when ownership is expected
(e.g., what (Heyman et al. 2004) refer to as a \quasi-endowment" eect).
2Other explanations for multiple bidding include bidders learning about valuations for an object over time (Cotton
2009, Hossain 2008, Rasmusen 2006), or bidders not understanding the bidding mechanism (Roth and Ockenfels 2002).
Bajari and Hortacsu (2004) review possible explanations of sniping, including the presence of asymmetrically informed
bidders (e.g., Wilson 1977), sequential auctions (Ely and Hossain 2009), tacit collusion among bidders (Roth and
Ockenfels 2002), or bidders who do not understand the bidding mechanism (Ockenfels and Roth 2006).
1The contribution of this paper is to show how the endowment eect can also drive sniping. The
intuition is as follows. From an ex ante perspective, players want to avoid the endowment eect,
as it can result in them increasing their bids above their initial valuations. By sniping, bidders
eectively commit to providing only one bid in the auction (at their initial valuation), and eliminate
the threat posed by the endowment eect.3 As long as the costs of waiting to bid are not too large,
sophisticated bidders (e.g., those who know they are susceptible to the endowment eect) snipe.
Na ve bidders (e.g., those who do not know they're susceptible), on the other hand, bid early and
possibly multiple times. The results are consistent with the empirical evidence that experienced
bidders are more likely to snipe, while less-experienced bidders are more likely to engage in multiple
bidding (e.g., Roth and Ockenfels 2002).
We illustrate how the endowment eect may cause sniping using a simple model. The intuition
should continue to hold in a more-general framework. For example, there may be more than two
bidders, auction may lasts for more than two periods, or not all players may be susceptible to the
endowment eect. We expect that the intuition from the model would also continue to hold with a
more general model of reference dependent preferences (e.g., Koszegi and Rabin 2006). Of course,
any of these generalizations may put further restrictions on the parameter space for which both
multiple bidding and sniping coexist in equilibrium. Additionally, the intuition will continue to
hold if (instead of suering from the endowment eect) players may \get caught up in" the bidding
process; by sniping, a player avoids getting caught up in a bidding war.
Model
There are two bidders in a second-price, winner-pay auction that lasts for two periods. Bidder i
values the auctioned item at vi  0, which is the independent realization of a random variable with
smooth distribution F and density f, where f(vi) > 0 if and only if vi 2 [0;  v]. Bidder i knows vi
and F, but not v i.4
There are two periods in which one may bid. Denote agent i's rst period bid B1i > 0, and
denote his second period bid B2i  B1i. If i does not bid in period 1, by default B1i = 0. If he
does not bid in period 2, by default B2i = B1i. In period 2, an agent can increase his bid or leave
it unchanged, but he cannot decrease his earlier bid. The agent with the highest B2i (i.e., the high
bidder) wins the prize and pays a price equal to B2 i. In a tie, each agent wins with probability
1=2; unless the tie is at B21 = B22 = 0, in which case neither agent wins the prize.
All players can submit a bid in period 1. However, they may not be able to submit a bid in
period 2. Let 1    2 (0;1) denote the probability an agent is able submit a second period bid.
When choosing B1i, agent i does not know whether he will be able to bid in period 2; although he
knows .5
3This is similar to commitment devises used to deal with other self-control issues such as present-biased preferences.
O'Donoghue and Rabin (1999) argue that sophisticated agents may limit their future choice sets when they know
their future selves could act in a way that reduces long-run welfare (from the current-period perspective).
4Subscript  i denotes i's opponent.
5There are many reasons why  > 0 is reasonable. It represents the possibility that something comes up resulting
2Players experience an endowment eect if they are the high-bidder in period 1; that is if B1i 
B1 i, and B1i 6= 0. Consistent with the behavioral literature, we formally model the endowment
eect as a form of loss aversion. If player i experiences the eect but does not eventually win the
item, he experiences a cost   where  > 0.
Although all players are susceptible to the endowment eect, not all players are aware of this
tendency. With probability  2 (0;1), a player is unaware of the endowment eect.6 Such a na ve
player chooses his initial bid unaware that any player may experience the endowment eect (i.e.,
as if  = 0). With probability 1   , a player is sophisticated and aware of the endowment eect.
Such a player takes both  and  into consideration when choosing his bids. This assumption is
consistent with the idea that experienced bidders may be more likely to recognize their tendency
to experience the endowment eect, while less-experienced bidders may not realized that such a
tendency exists.
When player i wins the item, he realizes payo Ui = vi   B2 i. When he does not win the
auction, he experiences payo Ui = 0 if he was never the high bidder, and payo Ui =   if he
experienced the endowment eect.
Player i is said to snipe if he waits to submit his rst bid until the second period; that is, if
B1i = 0 and, when he can bid in the second period, B2i > 0. A player is said to engage in multiple
bidding if he bids in the rst period, then raises his bid in the second period; that is, if B1i > 0
and, when he can bid in the second period, B2i > B1i.
Equilibrium
Using backward induction, the analysis solves for the perfect Bayesian equilibrium (PBE) of the
auction game.7
Period 2
Period 2 of the auction takes the form of a traditional Vickrey second-price auction, where all
bidders submit their (updated) valuations. If player i can submit a bid in the second period, in
equilibrium he submits B2i = Vi if he did not experience the endowment eect in period 1, and he
submits B2i = Vi +  if he did experience the endowment eect.
Period 1: na ve players
Na ve players believe they are bidding in an auction in which all players are fully rational, including
themselves. They play the equilibrium strategies from such a fully-rational game, and bid their
valuation in period 1. That is, for na ve bidders, B1i = vi. If B1i > vi, then he may end up paying
in the opportunity cost of returning to the auction being higher than the expected benet of returning, or that the
bidder has technical issues connecting to an online auction or submitting a bid.
6For a formal consideration of unawareness, see Dekel et al. (1998).
7Formally, the description of a PBE requires a denition of the beliefs. We generally ignore the beliefs in the
paper, as they should be obvious from the analysis, and o-equilibrium-path beliefs do not aect play.
3more than his valuation for the item. If B1i < vi (including B1i = 0), then he may not win the
item, even when it sells for less than his valuation. In either case, a na ve player has an incentive
to bid his valuation in the rst period.
Period 1: sophisticated players
Suppose player i is sophisticated. He knows that bidding in period 1 can result in him becoming
attached to the item and experiencing the endowment eect. By waiting to submit his rst bid until
period 2, a player can eectively commit to submit only one bid in the auction. This eliminates the
possibility that one experiences the endowment eect, which may result in him increasing his bid
and paying more than his valuation for the item, or in him not winning the item and experiencing
loss  . This is the benet of sniping.
However, sniping also comes with some costs. First, with probability  one is unable to submit
a bid in the second period. If a player does not bid in the rst period, the auction may end without
him submitting a bid. In this case, he does not win the item, even if the other player didn't bid
or bid less than his valuation. Second, waiting to bid increases the likelihood that an opponent
experiences the endowment eect in period 1. This in turn increases the opponent's expected
bid, which decreases the probability one wins the item when competing against the opponent, and
increases the expected price one must pay if he does win the item. These are the costs of sniping.
Whether a sophisticated agent snipes in equilibrium depends on the relative benets and costs
of doing so. The main result of the paper says that when the costs are not too large, sophisticated
players snipe, while na ve players increase their bids over the course of the auction.
Proposition 1 There exists a pure-strategy perfect Bayesian equilibrium in which na ve players
engage in multiple bidding, and, when  and  are not too large, sophisticated players snipe.
The parameter  is the probability one cannot submit a second period bid, and  is the prob-
ability one's opponent is na ve. When na ve players bid early and sophisticated bidders snipe, 
and  represent the costs associated with sniping. When the costs are small enough, sophisticated
players snipe. When the costs are too large, the sophisticated players bid in the rst period.
The analysis implies the following testable result.8
Corollary 2 If sophistication is positively correlated with experience, then sniping increases with
experience, and multiple bidding decreases with experience.
There is ample evidence in the empirical literature that this is true. Ockenfels and Roth (2006)
present eld evidence from eBay auctions that support this result. Ariely et al. (2005) present
similar evidence from lab experiments.9
8A formal proof is omitted, as it follows from the earlier analysis.
9Both Ockenfels and Roth (2006) and Ariely et al. (2005) also present evidence that sniping is more common
in eBay auctions than in Amazon.com auctions. The endowment eect model is also consistent with this evidence.
Where an eBay auction ends at a xed point in time, an Amazon.com auction is extended when someone submits a
bid near the end of the auction. This means that sniping to avoid the endowment eect only works in eBay auctions.
4Proof to Proposition 1
From the analysis in Section , we know that for na ve players, B1i = vi, and B2i = vi+ if B1i  B1 i and
B2i = vi if B1i < B1 i. A na ve player bids in the rst period, then if he experiences the endowment eect,
he attempts to increase his bid in the second period. That is, na ve players engage in multiple bidding. This
is always true.
It remains to be shown that there exists an equilibrium in which sophisticated bidders snipe when  and
 are low enough. It is straightforward to show that if i submits the high bid in period 1 and can submit a
bid in period 2, then B2i = vi + ; also, if he does not bid in period 1, he prefers B2i = vi. Given this, if i
chooses not to snipe, then he chooses B1i > 0 to maximize

R B1i
0 f(v i)[vi   v i]dv i + (1   )(1   )2
R vi+
0 f(v i)(vi   v i)dv i   (1   F(vi + ))

+(1   )vi + (1   )(1   )
R B1i
0 f(v i)[vi   v i]dv i   (1   F(B1i))

.
(1)
From the rst order conditions,
B1
i = vi +
(1   )(1   )
 + (1   )(1   )
.
Plugging B1
i into Eq. 1 gives the maximum expected utility if i does not snipe, which we denote EUi(B1i >
0). If he instead chooses to snipe, he expects
EUi(B1i = 0) = (1   )(1   )2 R vi
0 f(v i)(vi   v i)dv i + (1   )(1   )vi
+(1   )
R vi
0 f(v i)[vi   v i]dv i + (1   )2 R vi 
0 f(v i)(vi   v i   )dv i.
Both EUi(B1i > 0), and EUi(B1i = 0) are continuous functions in  and . Therefore, to show that
sophisticated bidders snipe when  and  are small enough, it is sucient to show that for any vi 2 [0;  v],
EUi(B1i = 0)   EUi(B1i > 0) > 0 when evaluated as  ! 0 and  ! 0. The condition simplies to
Z vi
0
f(v i)(vi   v i)dv i

 
Z vi+
0
f(v i)(vi   v i)dv i   (1   F(vi + ))

> 0.
Since
R vi
0 f(v i)(vi   v i)dv i >
R vi+
0 f(v i)(vi   v i)dv i the requirement is met. The strict inequality
implies a positive range of values  and  such that the condition still holds. For small enough  and ,
sophisticated bidders snipe.
References
Ariely, Dan, Axel Ockenfels, and Alvin E. Roth, \An experimental analysis of ending rules in Internet
auctions," RAND Journal of Economics, 2005, 36 (4), 890{907.
Bajari, Partick and Ali Hortacsu, \Economic Insights from Internet Auctions," Journal of Economic
Literature, 2004, 42, 457{486.
Cotton, Christopher, \Multiple bidding in auctions as buyers become condent of their private valua-
tions," Economics Letters, 2009, 104 (3), 148{150.
5Dekel, Eddie, Barton L. Lipman, and Aldo Rustichini, \Standard State-Space Models Preclude
Unawareness," Econometrica, 1998, 66 (1), 159{173.
Ely, Jerey C. and Tanjim Hossain, \Sniping and Squatting in Auction Markets," American Economic
Journal: Microeconomics, 2009, 1 (2), 68{94.
Heyman, James E., Yesim Orhun, and Dan Ariely, \Auction Fever: The Eect of Opponents and
Quasi-Endowment on Product Valuations," Journal of Interactive Marketing, 2004, 18 (4), 7{21.
Hossain, Tanjim, \Learning by bidding," RAND Journal of Economics, 2008, 39 (2), 509{529.
Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler, \Experimental Tests of the Endowment
Eect and the Coase Theorem," Journal of Political Economy, 1990, 98 (6), 1325{1348.
Koszegi, Botond and Matthew Rabin, \A Model of Reference-Dependent Preferences," Quarterly Jour-
nal of Economics, 2006, 121 (4), 1133{1165.
Ockenfels, Axel and Alvin E. Roth, \Late and multiple bidding in second price Internet auctions:
Theory and evidence concerning dierent rules for ending an auction," Games and Economic Behavior,
2006, 55, 297{320.
O'Donoghue, Ted and Matthew Rabin, \Doing It Now or Later," American Economic Review, 1999,
89 (1), 103{124.
Rasmusen, Eric B., \Strategic Implications of Uncertainty Over One's Own Private Value in Auctions,"
Advances in Theoretical Economics, 2006, 6 (1).
Roth, Alvin E. and Axel Ockenfels, \Last-minute Bidding and the Rules for Ending Second-Price
Auctions: Evidence from eBay and Amazon Auctions on the Internet," American Economic Review,
2002, 92 (4), 1093{1103.
Thaler, Richard, \Towards a Positive Theory of Consumer Choice," Journal of Economic Behavior and
Organization, 1980, 1 (1), 39{60.
Wilson, Robert, \A Bidding Model of Perfect Competition," Review of Economic Studies, 1977, 44, 511{
518.
6

A Bidding Model of Perfect Competition,&quot; Review of Economic Studies,

A Model of Reference-Dependent Preferences,&quot;

An experimental analysis of ending rules in Internet auctions,&quot;

Auction Fever: The Eect of Opponents and Quasi-Endowment on Product Valuations,&quot;

Doing It Now or Later,&quot; American Economic Review,

Economic Insights from Internet Auctions,&quot;

Experimental Tests of the Endowment Eect and the Coase Theorem,&quot;

Last-minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet,&quot; American Economic Review,

Late and multiple bidding in second price Internet auctions: Theory and evidence concerning dierent rules for ending an auction,&quot; Games and Economic Behavior,

Learning by bidding,&quot;

Multiple bidding in auctions as buyers become con of their private valuations,&quot; Economics Letters,

Sniping and Squatting in Auction Markets,&quot;

Standard State-Space Models Preclude Unawareness,&quot; Econometrica,

Strategic Implications of Uncertainty Over One's Own Private Value in Auctions,&quot;

Towards a Positive Theory of Consumer Choice,&quot;

Sniping to Avoid the Endowment Eect in Auctions

http://moya.bus.miami.edu/~ccotton/papers/EndowmentEffectAuctions.pdf

Sniping to Avoid the Endowment Eect in Auctions

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