Jump Bidding in English Auctions: an Experimental Study
Yuri Khoroshilov
University of Ottawa Telfer School of Management
55 E. Laurier, Ottawa, ON, K1H 2J1, Canada
e-mail: Khoroshilov@telfer.uottawa.ca
NOTE: this is research in progress. More experimental sessions will be conducted. All
results are preliminary. Any comments and suggestions are very much appreciated and will
be incorporated into the study. DO NOT CITE.
Acknowledgement: This research is supported by the SSHRC research grant in
management, business and finance.
1
1. Introduction
It is not uncommon for bidders in English auctions to place jump bids, i.e., to bid more
than the minimum required bid. One of the rationales behind such bidding behavior is
based on the signaling arguments. Namely, the first bidder with high value for the object
may want to place jump bid in order to signal potential competitors his high value, which,
in turn, may deter competitors from entering the auction. This argument is even more
appealing when bidders have some entry or bidding costs. It is believed (see Fishman,
1988; Hirshleifer and P’ng, 1989; Bhattacharyya, 2000) that signaling is the main reason
for jump bidding in takeover auctions (documented by Bradley, 1980; Betton and Eckbo,
2000), in which potential acquirers may face substantial transaction costs such as
investigation costs, entry costs, or bidding costs (Fishman, 1988; P’ng, 1986; Hirshleifer
and P’ng, 1989; Daniel and Hirshleifer, 1998; Bhattacharyya, 2000).
Most of the existing research in the area of takeover auctions has overlooked the seller’s
ability to change the reserve price during the course of the auction. This ability shares
many features with shill bidding, i.e., a situation when the seller bids on his own items
(Graham, Marshall, and Richard, 1990; Chakraborty and Kosmopoulou, 2004;
Kosmopoulou and De Silva, 2007). While shill bidding is usually prohibited, it is legal for
a target firm to reject an offer even when the offer is made substantially above the target’s
market value. This ability to reject the winning bid and to demand a higher price is similar
to shill bidding without concealing the bidder’s identity.
2
In auctions where the seller can alter the reserve price during the course of the auction,
signaling high value not only preempts potential competition but also reveals information
about the bidder’s value to the seller, who will consequently demand a higher price. The
unwanted revelation of this information diminishes the benefits of signaling and, under
some circumstances, makes signaling a suboptimal strategy (Dodonova and Khoroshilov,
2006; Dodonova, 2008).
Although jump bidding is particularly apparent in takeover auctions (Bradley, 1980;
Betton and Eckbo, 2000), jump bidding is also present in other type of auctions that use the
English auction design, such as many on-line auctions, or two-stage bidding auction
designs, such as government airway auctions (Easley and Tenorio, 2004; Grimm, Riedel,
and Wolfstetter, 2001; Borgers and Dustman, 2005, Crampton, 1997; Baldwin, Marshall,
and Richard, 1997). A more general theory of the use of jump bidding as a signaling
device in two-stage auctions with affiliated values was developed by Avery (1998).
Besides signaling, there are several alternative explanations for jump bidding. In some
instances, jump bidding can be explained by bidders’ anticipation of the seller’s hidden
reserve price, and, thus, by their desire to save time and effort by not placing bids which
will be refused outright (Dodonova and Khoroshilov, 2007). For a specific form of the
bidders’ value distribution function, jump biding can also be explained by strategic bidding
where bidders put jump bids to discourage other bidders with values in a specific region
from participation in the auction (Isaac, Salmon, and Zillante, 2007). Finally, jump bidding
3
may be explained by the bidders’ desire to speed up the auction (Isaac, Salmon, and
Zillante, 2005; Isaac and Schnier, 2007).
In this paper we discuss the results of an experimental study of jump bidding in English
auctions with entry cost and with “passive” and “active” sellers. In the first study we
investigate jump bidding behavior in standard private value English auctions with two
bidders and no reserve price. In the second study we conduct an experimental test of jump
bidding behavior in private value English auctions in which the seller can change the
reserve price during the course of the auction.
The main focus of this paper is to test whether jump bidding can be, at least partially,
explained by signaling arguments and how it is affected by the seller’s ability to change
reserve price during the course of the auction. To achieve this goal, and, in particular, to
separate signaling arguments from impatience, we conducted a simplified version of
English auctions, in which only one (the first) bidder is able to place only one (initial)
jump bid and the second bidder must make an entry decision based on the value of the
opening bid. After the entry decision is made, we “force-run” the auction, i.e., we
pronounce the bidder with the largest value to be the winner at the price equal to the
maximum between the other bidder’s value, the reserve price, and the opening bid.
The rest of the paper is organized as follows. In part 2 we discuss the results of the
experimental study for auctions with zero reserve price conducted over e-mail in which
subjects were asked to choose a menu of actions. In part 3 we present the results of a
4
similar study conducted in the laboratory setting in which subjects were actually engaged
in the auction game. In part 4 we discuss the proposed experiments for auctions with
reserve price under two scenarios: when the seller cannot change the reserve price during
the course of the auction and when he can do so. Note that this is work in progress and we
did not conduct any experiments with reserve price yet. In part 5 we conclude.
2. No-reserve auction: e-mail study
The first study is designed to test the signaling hypothesis in no-reserve English auctions
with two bidders who face entry costs. To do so, we conducted experiments with two
groups of students in which subjects were asked to provide their complete strategies, i.e.,
to provide their strategies at each possible state of the world. The auction design used for
this study was as follows:
The game:
Two bidders (bidder #1 and bidder #2) participate in an auction for a fictional item. At the
beginning of the auction, bidder #1 receives a randomly drawn value (S1) for the item. This
value is uniformly distributed on the interval between $0 and $20. He pays a nonrefundable entry fee F (mandatory) and places his initial bid (B1). Based on the value of
this bid, bidder #2 decides if he wants to enter the auction or not. If bidder #2 does not
enter the auction, bidder #1 wins the item for the price of his initial bid B1. If bidder #2
enters the auction, he pays a non-refundable entry fee F and receives a randomly drawn
value (S2) for the item. This value is uniformly distributed on the interval between $0 and
5
$20. After that, it is assumed that bidders will be participating in a thermometer English
auction, and will bid up to their values. This step (thermometer English auction) is
substituted by its outcome under the optimal bidding assumption. In particular, the bidder
with the highest value is pronounced a winner and the final price is set to the maximum
between the initial bid and the losing bidder’s value.
The experiment consisted of three rounds. In each round subjects were asked to provide
their strategies in each state of the world. Namely, they were asked to specify the size of
the initial bid that they will place if they will play for bidder #1 as a function of S1. For this
purpose, the possible value of S1 was divided into 20 intervals (from $0 to $1, from $1 to
$2, …, from $19 to $20) and subjects were asked to specify B1 for each of the intervals.
They were also asked to specify their strategies for bidder #2 (“enter” or “do not enter”) as
a function of B1. Subjects were asked to provide these strategies for 4 different entry cost
games: F=$1, $2, $3, and $4. At the end of each round subjects were given the sample
statistics for the previous round (i.e., the average bid B1 as a function of S1 and the
probability that bidder #2 enters as a function of B1) and the best ex post strategy, i.e., the
strategy, that will earn the maximum average profit if played against all the strategies
submitted in that round. Namely, students were given the best ex post strategy (against
strategies submitted by all subjects in the given round) for bidder #1 as a function of S1 and
the expected payoff for bidder #2 as a function of B1. In addition, subjects in the second
group were provided with a strategy form that specifies which strategies always result in
negative payoff. The latter was designed to make subjects to better understand the game
and to prevent irrational behavior that was observed in the first group which may be due to
6
the complexity of instructions. In total, there were 36 subjects in the first group and 34
subjects in the second group participated in round 1 and these numbers decreased to 24 and
29 in round 3 respectively.
Subjects were paid based on how well their strategies performed against strategies of all
other players. Namely, in each round (1, 2, 3) and for each auction design (F=$1, $2, $3,
$4) we computed the average profit for each subject’s strategy (separately for bidder #1
strategy and bidder #2 strategy) played against all strategies of other subjects (bidder#2
and bidder#1 strategies respectively). The subject’s total compensation was set to $15
participation compensation plus 50% of the all the money their strategies earned.
Figures 1.1a and 1.2a present the average strategies for bidders #1 (average bid as a
function of S1) and bidders #2 (probability to enter as a function of B1) for the first group
in the first round respectively. Figures 1.1b, 1.2b, 1.1c, and 1.2c present the average
strategies for rounds 2, and 3 respectively. Figures 2.1a, 2.2a, 2.1b, 2.2b, 2.1c, 2.2c present
the corresponding strategies for the second group. Table 1 presents the best ex post
strategies for bidder #1 and bidder #2 in all three rounds for group 1. Table 2 provides the
corresponding strategies for group 2.
7
Figure 1.1a: Average jump bid in group 1 round 1
$9
$8
$7
B1
$6
$5
$4
$3
$2
$1
$0
0-1
2-3
4-5
6-7
8-9
10-11
12-13
14-15
16-17
18-19
S1
F=1
F=2
F=3
F=4
Figure 1.2a: Entry proportion in group 1 round 1
100%
90%
Probability to enter
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
B1
F=1
F=2
F=3
F=4
8
Figure 1.1b: Average jump bid in group 1 round 2
$5
$4
B1
$3
$2
$1
$0
0-1
2-3
4-5
6-7
8-9
10-11
12-13
14-15
16-17
18-19
S1
F=1
F=2
F=3
F=4
Figure 1.2b: Entry proportion in group 1 round 2
100%
90%
Probability to enter
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
B1
F=1
F=2
F=3
F=4
9
Figure 1.1c: Average jump bid in group 1 round 3
$4
B1
$3
$2
$1
$0
0-1
2-3
4-5
6-7
8-9
10-11
12-13
14-15
16-17
18-19
S1
F=1
F=2
F=3
F=4
Figure 1.2c: Entry proportion in group 1 round 3
100%
90%
Probability to enter
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
B1
F=1
F=2
F=3
F=4
10
Figure 2.1a: Average jump bid in group 2 round 1
$5
$4
B1
$3
$2
$1
$0
0-1
2-3
4-5
6-7
8-9
10-11
12-13
14-15
16-17
18-19
S1
F=1
F=2
F=3
F=4
Figure 2.2a: Entry proportion in group 2 round 1
100%
90%
Probability to enter
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
B1
F=1
F=2
F=3
F=4
11
Figure 2.1b: Average jump bid in group 2 round 2
$3
B1
$2
$1
$0
0-1
2-3
4-5
6-7
8-9
10-11
12-13
14-15
16-17
18-19
S1
F=1
F=2
F=3
F=4
Figure 2.2b: Entry proportion in group 2 round 2
100%
90%
Probability to enter
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
B1
F=1
F=2
F=3
F=4
12
Figure 2.1c: Average jump bid in group 2 round 3
$3
B1
$2
$1
$0
0-1
2-3
4-5
6-7
8-9
10-11
12-13
14-15
16-17
18-19
S1
F=1
F=2
F=3
F=4
Figure 2.2c: Entry proportion in group 2 round 3
100%
90%
Probability to enter
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
B1
F=1
F=2
F=3
F=4
13
Table 1: Ex-post optimal strategies in group 1
Round 1
Round 2
F=1
F=2
F=3
F=4
F=1
F=2
F=3
F=4
Round 3
F=1
F=2
F=3
F=4
Bidder #1
B1=0
B1=0
B1=0
B1=0
B1=0 if S1≤3
B1=1 if S1>3
B1=0
B1=0 if S1≤5
B1=1 if 5<S1≤6
B1=2 if S1>6
B1=0 if S1≤3
B1=1 if S1>3
B1=0
B1=0 if S1≤15
B1=5 if S1>15
B1=0 if S1≤4
B1=2 if 4<S1≤15
B1=4 if S1>15
B1=0 if S1≤2
B1=1 if 2<S1≤17
B1=3 if S1>17
Bidder #2
Enter if and only if B1≤9
Enter if and only if B1≤5
Enter if and only if B1≤2
Enter if and only if B1=0
Enter if and only if B1≤9
Enter if and only if B1≤4
Enter if and only if B1=0
Enter if and only if B1=0
Enter if and only if B1≤9
Enter if and only if B1≤2
Enter if and only if B1≤1
Enter if and only if B1=0
14
Table 2: Ex-post optimal strategies in group 2
Round 1
F=1
F=2
F=3
F=4
Round 2
F=1
F=2
F=3
F=4
Round 3
F=1
F=2
F=3
F=4
Bidder #1
B1=0
B1=0 if S1≤11
B1=1 if S1>11
B1=0 if S1≤6
B1=2 if 6<S1≤11
B1=3 if S1>11
B1=0 if S1≤2
B1=1 if S1>2
B1=0 if S1≤5
B1=1 if S1>5
B1=0 if S1≤4
B1=1 if 4<S1≤10
B1=5 if S1>10
B1=0 if S1≤2
B1=1 if 2<S1≤5
B1=2 if S1>5
B1=0 if S1≤2
B1=1 if S1>2
B1=0 if S1≤13
B1=1 if S1>13
B1=0 if S1≤2
B1=1 if 2<S1≤6
B1=2 if 6<S1≤9
B1=4 if S1>9
B1=0 if S1≤2
B1=1 if 2<S1≤3
B1=2 if 3<S1≤11
B1=4 if S1>11
B1=0 if S1≤1
B1=1 if S1>1
Bidder #2
Enter if and only if B1≤7
Enter if and only if B1≤4
Enter if and only if B1=0
Enter if and only if B1=0
Enter if and only if B1≤5
Enter if and only if B1=0 or B1=4
Enter if and only if B1=0
Enter if and only if B1=0
Enter if and only if B1≤5
Enter if and only if B1≤1
Enter if and only if B1=0
Enter if and only if B1=0
15
As it can be seen from this data, in almost all rounds the initial bid positively depends on
the bidder’s value while the probability that the second bidder enters the auction negatively
depends on the value of the initial bid. In addition, the strategies of the first bidders in
many rounds result in the “best strategy” of the second bidder in which he enters if and
only if the initial bid is smaller than some threshold.
Finally, the strategies of the second bidders’ warrant a signaling behavior of bidder #1
whose best strategy is to place a jump bid if and only if his value is above some threshold.
Sometimes, the jump bidding structure involves jumps of two or three different sizes: high
jumps for bidders with extremely high values and lower jumps for bidders with moderately
high values. We also observed that higher entry fee makes bidders #2 less willing to enter,
and also decreases the value of initial bids.
3. No-reserve auction: laboratory study
This study is also designed to test the signaling hypothesis in no-reserve English auctions
with two bidders who face entry fees. In this study 18 subjects played the same game as
described above with the exception that the values S1 and S2 were distribute on [$0, $200]
instead of [$0.20] interval and the entry fee was set to $25. For each round subjects were
randomly divided into pairs and they were randomly assigned their roles (bidder #1 and
bidder #2). Each subject has participated in 50 auctions and his final payment was equal to
$25 participation compensation plus the average (per round) amount of money he won
during the session. The experiment was programmed and conducted with the software zTree (Fischbacher, 2007).
16
Figure 3 presents the relationship between the first bidder’s value S1 and the size of the
initial bid B1. Figure 4 presents the proportions of the second bidders who decided to enter
the auction as a function of the initial bid posted by the first bidder. For these figures we
combined the data in intervals of size $10 and computed the average bid (for bidder #1)
and proportions to enter (for bidder #2). Similar to the “e-mail” study data, the initial bid
positively depends on the first bidder’s value while the probability to enter fro the second
bidder negatively depends on the initial bid submitted by bidder #1. The OLS regression
estimation of the effect of S1 on B1 shows a positive significant (at 1% level) slope of
0.2791. The logit model estimation of the probability that the second bidder enters as a
function of B1 shows a negative significant (at 1% level) slope of -0.0477. More
observations that we will receive in future experiments will allow us to use smaller
intervals.
Using the average data for $10-wide intervals, we found that, given the second bidder
strategies, the best strategy of the first bidder in this experiment would be: bid B1=$0 if
S1≤$40, bid B1=$20 if $41≤S1≤$67, and bid B1 =$40 if $68≤S1. Given the first bidder
strategies and their realized values of the object (S1), the best strategy of the second bidder
in this experiment would be to enter if and only if B1<50. Furthermore, for $20≤B1<$50,
the second bidder is almost indifferent between entering and not entering the auction
(Figure 5 presents the expected profit of bidder #2 from entering the auction for different
values of B1). This data allows us to say that observed behavior is close to a jump bidding
equilibrium.
17
100 and
above
90-100
80-90
70-80
60-70
50-60
40-50
30-40
20-30
10-20
0-10
Probability to enter
190-200
180-190
170-180
160-170
150-160
140-150
130-140
120-130
110-120
100-110
90-100
80-90
70-80
60-70
50-60
40-50
30-40
20-30
10-20
0-10
B1
Figure 3: Average jump bid (laboratory study)
$60
$50
$40
$30
$20
$10
$0
S1
Figure 4: Entry proportion (laboratory study)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
B1
18
Figure 5: Expected profit of the second bidder
from entering (laboratory study)
$25
100 and
above
90-100
80-90
70-80
60-70
50-60
40-50
30-40
20-30
-$5
10-20
$5
0-10
Profit from entering
$15
-$15
-$25
B1
19
The average profits of bidder #1, bidder #2 and the seller were $14.1, $11.64, and $59.09.
On average, auctions generated $84.83 of total welfare (defined as a sum of all parties’
profits). Although bidders #1 generated higher profit than bidders #2, the difference is not
statistically significant. Future experiments will allow us to investigate this relationship
further.
In a comparable auction with entrance fee in which jump bidding is not allowed, the
optimal strategies for bidder #2 is to enter. In this case, the average profits for each bidder
are $8.33, the profit of the seller is $66.66 and the total welfare is $83.33. Thus, existing
data shows that jump bidding does not affect efficiency, but reallocate profits from the
seller to the bidders. Future experiments will allow us to investigate this relationship
further.
4. Auction with reserve price: laboratory study
This study is designed to test the signaling hypothesis in auctions where the seller is able to
change the reserve price during the course of the auction. This is work-in-progress and we
did not conduct any sessions yet. In this study subjects will be divided into two groups and
will play the following games:
The game for group #1:
Two bidders (bidder #1 and bidder #2) and a seller participate in an auction for a fictional
item. At the beginning of the auction the seller sets a secret the reserve price R (no one is
20
able to observe R until the end of the auction). After that, bidder #1 pays a non-refundable
entry fee F (mandatory) and receives a randomly drawn value (S1) for the item. This value
is uniformly distributed on the interval between $0 and $200. Based on this value, he
places his initial bid (B1). Based on the value of this bid, bidder #2 decides if he wants to
enter the auction or not. If bidder #2 does not enter the auction, bidder #1 wins the item for
the price that is equal to the maximum between his initial bid B1 and the reserve price R. If
bidder # 2 enters the auction, he pays a non-refundable entry fee F and receives a randomly
drawn value (S2) for the item. This value is uniformly distributed on the interval between
$0 and $200. After that, it is assumed that bidders will be participating in a thermometer
English auction, and will bid up to their values. This step (thermometer English auction) is
substituted by its outcome under the optimal bidding assumption. In particular, the bidder
with the highest value is pronounced a winner and the final price is set to the maximum
between the reserve price, the initial bid, and the losing bidder’s value. Finally, after the
winner and the final price is determined, the winner receives the item and pays the abovedetermined price to the seller if and only if his value is greater than or equal to the final
price (i.e., if and only if his value is greater than or equal to the reserve price set by the
seller). If the winner’s value is less than the final price, no sale takes place.
The game for group #2:
Similar as the game for group #1 except that the seller sets his reserve price R after he
observes the initial bid B1 placed by the first bidder.
Results we expect to receive:
21
We expect to see signaling in group #1 and negative dependence of R on B1 in group 2.
We also expect to see lower B1 in group 2 than in group 1 and weaker dependence of the
probability to enter on B1. Other parameters to look at: efficiency, expected revenue and
bidders’ profits.
5. Conclusion
This paper presents the results of experimental study of signaling and jump bidding in
English auctions with entrance cost. It investigates two auction designs: auction with no
reserve of fixed reserve price and auctions in which the seller can change the reserve price
during the course of the auction. This is research in progress and more sessions will be
conducted. Current data shows support for the signaling hypothesis for auctions with no
reserve price. No sessions for auctions with flexible reserve price have been conducted yet.
22
Appendix A: Subjects’ instructions for “no-reserve auction: e-mail study”
The auction game:
• 2 bidders (bidder #1 and bidder #2) participate in the auction for a fictional item.
• Bidder #1 receives a randomly drawn value (S1) for the item. This value is
uniformly distributed on the interval between $0 and $20
• Bidder # 1 pays a non-refundable entry fee F (mandatory) and places his first bid
(B1). The first bid can be any INTEGER number between $0 and $19 (note:
bidding $0 is allowed) and it must satisfy B1≤S1
• Bidder # 2 observes the initial bid placed by the first bidder and must decide if he
wants to enter the auction or not.
o If bidder # 2 does not enter the auction, bidder #1 wins the item for the price
of his first bid (B1) and immediately sells it to the auctioneer for S1. As a
result, in this game
Bidder #1 receives $(S1-B1-F)
Bidder #2 receives $0
o If bidder # 2 enters the auction, he pays a non-refundable entry fee F and
receives a randomly drawn value (S2) for the item. This value is uniformly
distributed on the interval between $0 and $20. After that, the bidder with
the highest value wins the auction for the price that is equal to the
maximum between the initial bid and the value of the loosing bidder. In
particular:
If S1>S2, then bidder #1 wins the auction for the price of
max(B1,S2). As a result, in this game
• Bidder #1 receives $(S1-max(B1,S2)-F)
• Bidder #2 receives $-F (note that bidder #2 looses money)
If S1≤S2, then bidder #2 wins the auction for the price of
max(B1,S1). As a result, in this game
• Bidder #1 receives $-F (note that bidder #1 looses money)
• Bidder #2 receives $(S2-max(B1,S1)-F)
Example1:
• Assume F=$1, S1=$12.73 and bidder #1 decides to place the first bid of $4.
• Assume bidder #2, after observing the initial bid of $4, decides not to enter
• Thus, bidder #1 wins the object for $4 and the profits are:
o Bidder #1: $12.73-$4-$1=$7.73
o Bidder #2: $0
Example2:
• Assume F=$1, S1=$12.73 and bidder #1 decides to place the first bid of $0.
• Assume bidder #2, after observing the initial bid of $0, decides not to enter
• Thus, bidder #1 wins the object for $0 and the profits are:
o Bidder #1: $12.73-$0-$1=$11.73
o Bidder #2: $0
Example3:
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•
•
•
Assume F=$1, S1=$12.73 and bidder #1 decides to place the first bid of $4.
Assume bidder #2, after observing the initial bid of $4, decides to enter. Assume
also that , after entering, he receives S2=$7.51
Thus, bidder #1 wins the object for max($4, 7.51)=$7.51 and the profits are:
o Bidder #1: $12.73-$7.51-$1=$4.24
o Bidder #2: $-1
Example4:
• Assume F=$1, S1=$12.73 and bidder #1 decides to place the first bid of $4.
• Assume bidder #2, after observing the initial bid of $4, decides to enter. Assume
also that , after entering, he receives S2=$16.85
• Thus, bidder #2 wins the object for max($4, 12.73)=$12.73 and the profits are:
o Bidder #1: $-1
o Bidder #2: $16.85-$12.73-$1=$3.12
Instructions
• You must specify your strategies as bidder #1 and as bidder #2 for the auction
game described above for four different values of entree fee F: $1, $2, $3, and $4
• As bidder #1, you must specify B1 as a function of S1 for 20 different intervals of
possible values of S1: ($0,$1), ($1,$2), ($2,$3),…,($19,20).
o B1 must be an integer number (B1=$0 is allowed)
o B1 must be below S1, i.e., if S1=$15.43, B1 must be an integer number
between $0 and $15 ($0≤B1≤$15)
• As bidder #2, you must specify your entry decision (“enter”, or “do not enter”) as a
function of B1
• For each four auction designs (with F=1, 2, 3, and 4), your will play against all
other participants and your expected profit as “bidder #1” and “bidder #2” for each
auction design will be computed.
How to submit your strategy:
• Attached, you can find an excel file. In all cells with “**” you must substitute “**”
with your strategy.
• In cells with “NAME” enter your first and last name
• In cells with “E-Mail” enter your e-mail address
• In lines 3-6 columns D-W you must enter your strategy as bidder #1 for four
different auction designs (F=1, 2, 3, 4) as a function of S1. For example, if in
auction with F=$1, after observing S1=$2.34 you would like to place B1=0, put 0
in cell F3.
• In lines 12-15 columns D-W you must enter your strategy as bidder #2 for four
different auction designs (F=1, 2, 3, 4) as a function of B1. Please, enter 0 if your
strategy is “do not enter” and enter 1 if your strategy is “enter”. For example, if in
auction with F=$4, after observing B1=$4 you do not want to enter, put 0 in cell
H15.
• Please, read carefully all the instructions!!! In particular, for rows 3-6 remember
that B1 must be integer and must satisfy $0≤B1≤$S1. For rows 12-15 remember to
use 0 for “do not enter” and 1 for “enter”. If you will not follow these
24
•
instructions, you will be excluded from this study and will receive only a
compensation earned for the preceding rounds (as described below) for which you
have submitted your strategies correctly
Please, rename the file as “YourLastName_Round1.xls”, where instead of
“YourLastName” put your last name, and e-mail it to
experiments@telfer.uottawa.ca as e-mail attachment no later than 11:59pm on
Thursday, February 5.
Your compensation:
• You will receive $5 for participation in each round (total of up to $15 for
participation). In addition, you will receive a bonus as follows:
• Your expected profits as bidder #1 and bidder #2 for all 4 auction designs will be
added up and you will receive $0.50 CAD for each $1 you won in the games. For
example, if your expected profits as bidder #1 in auctions with F=1,2,3,4 are $7.63,
$6.87, $6.22, $5.97 and your expected profits as bidder #2 in auctions with
F=1,2,3,4 are $3.02; $2.15; $1.29; $0.79, then your total “profit” in “experimental
dollars” will be (7.63+6.87+6.22+5.97+3.02+2.15+1.29+0.79=$33.94
“experimental dollars”. Thus, you bonus in CAD will be 33.93/2=$16.96
• I expect the average compensation to be around $40 per student, however, your
individual compensation will depend on how well you’ll play.
• At any time you can withdraw from this study in which case you will receive $5 for
each round in which you have participated plus any bonuses earned up to that date.
If I will not receive your strategy form on time regardless of the reason or I will
receive an incorrectly filled strategy form, it will be considered as your desire to
withdraw from the study.
• You will need to come to my office to pick up your money after the study is
completed (you can authorize your friend to pick up your money for you). Times
and dates will be e-mailed after the end of the last round. Your total payoff will be
rounded to the nearest dollar.
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Appendix B: Subjects’ instructions for “no-reserve auction: laboratory study”
You will play 50 auction games (as described below). For each game students will be
randomly divided into pairs and, in each pair, one of the students will be named “bidder
#1” and the other will be named “bidder #2”. Your goal is to make as much money as
possible. At the end of the experiments you will be paid $25 for participation plus the
average amount of money you win during these 50 games. Please, follow instructions on
your screen. Note that, from time to time, you may have to wait until all the students
complete the round. If you will have any questions – please, ask me at any time.
The auction game:
The game is a simplified version of an auction with two bidders. The auction proceeds as
follows;
•
•
•
Bidder #1 pays a non-refundable entry fee of $25 and learns his “resale value” $S1 of
the object he is bidding for. S1 is a randomly drawn number uniformly distributed
between $0.01 and $200
After learning S1 bidder #1 must place an opening bid B1 between $0 and $S1
Bidder #2 observes B1 and must decide if he wants to enter the auction or not. (Note
that bidder #2 cannot see S1 at this point)
Now, two scenarios are possible:
1) If bidder #2 does not enter the auction, then bidder #1 wins the object for the value of
his initial bid. As a result, bidder #1 earns $(S1-B1-25) and bidder #2 earns $0 for this
round.
2) If bidder #2 enters the auction, then he pays a non-refundable entry fee of $25 and
learns his “resale value” $S2. It is assumed that at this point bidders will start the standard
bidding process and will bid optimally, i.e., will bid as long as the current price is lower
than the bidder’s resale value. To simplify the game, this “bidding process” will be
substituted by its outcome. Namely:
2a) If S1> S2, then bidder #1 wins the object. Since the auction will start from B1 and
bidder #2 will bid up to S2, the final price will be max(B1,S2). As a result, bidder #1
earns $(S1-max(B1,S2)-25) and bidder #2 loses $25.
2b) If S1≤ S2, then bidder #2 wins the object. Since the auction will start from B1 and
bidder #1 will bid up to S1, the final price will be max(B1,S1)=S1. As a result, bidder
#2 earns $(S2- S1-25) and bidder #1 loses $25.
26
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