Online Appendix for“The net eﬀect of advice on strategy-proof
mechanisms: An experiment for the Vickrey auction”
Takehito Masuda
Ryo Mikami
Toyotaka Sakai
Shigehiro Serizawa
Takuma Wakayama
October 5, 2021

Contents
A Statistics used in hypotheses testing
A.1 Advice eﬀect on sincere bidding . . . . . . . . . . . . . . . . . . . . . .
A.2 Advice eﬀect on eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
4

B Binary eﬃciency

5

C Analysis on the ﬁrst-period data

7

D How did subjects perceive advice?

9

E Additional table

11

F Experimental instructions (VA and VN)
F.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F.2 Auction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F.2.1 Procedure in each period . . . . . . . . . . . . . . . . . . . . . .
F.2.2 Earnings calculation . . . . . . . . . . . . . . . . . . . . . . . .
F.3 Rewards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12
12
12
12
13
16

G Experimental instructions (PA and PN)
G.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
G.2 Auction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
G.2.1 Procedure in each period . . . . . . . . . . . . . . . . . . . . . .
G.2.2 Earnings calculation . . . . . . . . . . . . . . . . . . . . . . . .
G.3 Rewards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19
19
19
19
20
23

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H Text of advice (VA and PA)

26

I

27
27
28

Auction screens and procedures (VA, VN, PA, and PN)
I.1 Bidding screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I.2 Auction results screen . . . . . . . . . . . . . . . . . . . . . . . . . . .

J Quiz (VA, VN, PA, and PN)

29

K Post-experiment survey (VA and PA)

31

L Post-experiment survey (VN and PN)

33

M Experimental instruction (AA and AN)
M.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M.2 Auction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M.2.1 Procedure in each period . . . . . . . . . . . . . . . . . . . . . .
M.2.2 Earnings calculation . . . . . . . . . . . . . . . . . . . . . . . .
M.3 Rewards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35
35
35
35
37
40

N Text of advice (AA)43

O Auction screens and procedures (AA and AN)
O.1 Screen before beginning the auction . . . . . . . . . . . . . . . . . . . .
O.2 Decision-making screen . . . . . . . . . . . . . . . . . . . . . . . . . . .
O.3 Conﬁrmation screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44
44
44
47

P Quiz (AA and AN)

48

Q Post-experiment survey (AA)50

R Post-experiment survey (AN)52

S Individual bidding data

54

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A

Statistics used in hypotheses testing

A.1

Advice eﬀect on sincere bidding

Suppose that sincere bidding behavior in treatment j ∈ {VA, VN, PA, PN, AA, AN} isa realization of a random variable Xj with the Bernoulli distribution that takes thevalue of 1 (= sincere bidding) with the success rate of pj . That is,1 with prob. p ,jXj ≡0 with prob. 1 − p .
j

Let X j denote the sample mean for nj realizations of Xj and let
Sj ≡X j (1 − X j ).
njHereinafter, superscripts “All,” “Per,” and “Im” correspond to all subjects, the subjects
whose quiz scores are perfect, and those whose quiz scores are imperfect, respectively.
Capital and small letters indicate random variables and realized values, respectively.
• Result 2 and Result 9: Given j ∈ {V, P, A} and h ∈ {All, Per, Im}, let Yjh ≡´³ hh
X jA − X jN . The test statistic is
Yjh − E(Yjh )Yejh ≡ q
,
h
h
SjA
+ SjN
where E is the expectation operator. By the central limit theorem, Yjh approximately
follows a standardized normal distribution.32¡¢• Result 3: Let ZVAll = YVAll − YPAll . The test statistic is
Z All − E(ZVAll )ZeVAll ≡ p All V All
.
All
All
SVA + SVN + SPA
+ SPN
¡
¢
• Result 10: Let ZAAll = YAAll − YVAll . The test statistic is
ZAAll − E(ZAAll )
All
e
p
ZA ≡
.
All
All
All
All
SAA
+ SAN
+ SVA
+ SVN
32

See page 255 of Jacquemet and L’Haridon (2018) for the construction of our test statistics.

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¡¢• Result 4 and Result 11: Given j ∈ {V, A}, let Wj = YjPer − YjIm . The test
statistic is
Wj − E(Wj )fj ≡ q
W
.
Per
Per
Im
Im
SjA
+ SjN
+ SjA
+ SjN

A.2

Advice eﬀect on eﬃciency

Suppose that the eﬃciency ratio r in treatment j ∈ {VA, VN, PA, PN, AA, AN} is arealization of a random variable Rj with mean E(Rj ) ∈ [0, 1] and variance Var(Rj ).
Let Rj denote the sample mean for nj0 realizations of Rj . Let
Pnj
Tj ≡

2
0
k=1 (Rjk − Rj ) /(nj − 1).
n0jSuperscripts “All,” “F13,” and “L12” correspond to all periods, the former 13 periods(periods 1–13), and the latter 12 periods (periods 14–25), respectively.
• Result 5 and Result 12: Given j ∈ {V, P, A} and h ∈ {All, F13, L12}, let Ujh =´³ hh
RjA − RjN . The test statistic is
Ujh − E(Ujh )he
Uj ≡ q
.
h
h
TjA
+ TjN
¡
¢
• Result 6: Given h ∈ {All, F13, L12}, let Qh = UVh − UPh . The test statistic is
Qh − E(Qh )eh ≡ p
Q
.
h
h
h
h
TVA
+ TVN
+ TPA
+ TPN

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BBinary eﬃciency

Table 19 summarizes the frequencies of realization of eﬃcient allocation by treatments
and periods. Thereafter, we apply normal approximation the same as that we presented
in Section 3.2. Suppose that the achievement of eﬃcient allocation in treatment j ∈{VA, VN, PA, PN, AA, AN} is a realization of a random variable Ej with a Bernoulli
distribution that takes the value of 1 (= eﬃcient) with a success rate of qj . That is,1 with prob. q ,jEj ≡0 with prob. 1 − q .
j

Let E j denote the sample mean for nj0 realizations of Ej and let
Γj ≡E j (1 − E j ).
n0j

From Table 19, we ﬁnd a signiﬁcant increase in the eﬃciency of the Vickrey auction
for all periods and the former 13 periods. In contrast to the eﬃciency measure used in
the main text, we also ﬁnd that the advice eﬀect on eﬃciency exists in the pay-your-bid
auction for all periods only. Overall, it turns out that the net advice eﬀect disappears
if we use the binary eﬃciency as a measure of eﬃciency.
In Table 19, we have signiﬁcance at the cells of (AA−AN, All periods) and (AA−AN,
Periods 1–13). In sum, Hypothesis 5’ is rejected in both the data all periods and thedata of the former 12 periods.

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Online Appendix – Page 6

Vickrey(1)
Pay-your-bid(2)
Ausubel(3)
VA
VN
VA − VN
PA
PN
PA − PN (1) − (2)AAAN
AA − AN (3) − (1)
0.779
0.705
0.074∗∗∗ 0.823
0.783
0.039∗∗ 0.035
0.878
0.839
0.039∗∗ −0.035(0.415) (0.457)(0.382) (0.412)(0.328) (0.368)
0.744
0.644
0.099∗∗∗ 0.823
0.782
0.041
0.059
0.850
0.794
0.057∗−0.042(0.437) (0.480)(0.383) (0.414)(0.357) (0.406)
0.817
0.771
0.047
0.822
0.785
0.038
0.009
0.907
0.892
0.015
−0.031(0.387) (0.421)(0.383) (0.412)(0.291) (0.311)

Notes: ∗ denotes signiﬁcant at the 10% level, ∗∗ at the 5% level, and ∗∗∗ at the 1% level.

Periods 14–25

Periods 1–13

All periods

Data

Table 19: Binary eﬃciency by treatments and periods.

C

Analysis on the ﬁrst-period data

In this section, we restrict our attention to the ﬁrst period only and use both units’ data.
As shown in Table 20, Hypothesis 1, Hypothesis 2, and Hypothesis 3 are again rejected
at the 5% signiﬁcance level except for the cases including imperfectly scored subjects inthe pay-your-bid auction, where the sample size is smaller than 30, while Hypothesis 4
is not (p = 0.471). Moreover, we reject Hypothesis 3’ at the 5% signiﬁcance level, while
we fail to reject Hypothesis 1’ (p = 0.132).

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Online Appendix – Page 8

Vickrey(1)
VA
VN
VA − VN
0.468
0.188
0.281∗∗∗(0.501) (0.392)
0.512
0.233
0.279∗∗∗(0.503) (0.427)
0.381
0.111
0.270∗∗∗(0.492) (0.319)

Pay-your-bid
PA
PN
0.123
0.021
(0.330)(0.143)0.138
0.026(0.346)(0.161)0.045b)0.000(0.213)(0.000)0.167∗∗
0.224∗∗

0.112∗∗∗
0.045(2)
PA − PN (1) − (2)0.102∗∗∗ 0.178∗∗∗

AusubelAA
ANAA − AN
0.319
0.237
0.083
(0.470) (0.428)
0.297
0.231
0.067
(0.463) (0.427)
0.343
0.243
0.100
(0.482) (0.435)

Notes: a) ∗ denotes signiﬁcant at the 10% level, ∗∗ at the 5% level, and ∗∗∗ at the 1% level; and b) The number of observations is no more than 30.

Imperfect Score

Perfect Score

All

Data

Table 20: Frequency of sincere bidding in period one by treatments and quiz scores.

D

How did subjects perceive advice?

We examine how many subjects believed the advice in VA by employing a post experimental questionnaire. The questionnaire asks subjects whether they believe the advice,
and if yes, since when they started believing it. Subjects chose one from four answers:(a) Believed the advice before practice periods;(b) Believed the advice after practice periods but before real periods;(c) Believed the advice during real periods; and(d) Never believed.
In VA, the number of subjects who chose (a), (b), (c), and (d) is, respectively, 13, 14,
14, and 22. Thus, in VA, 41 subjects believed the advice, and 22 did not.
We categorize the subjects in VA into two groups—agents who believed (a, b, c)and agents who never believed (d)—and run normal approximation parametric tests
for group comparison. We obtain two reasonable results:
1. The VA subjects who believed the advice bid signiﬁcantly more sincerely compared with those who never believed the advice (60.2% and 22.2%, respectively;z = 22.97, p < 0.001); and2. The rate of sincere bidding among the VA subjects who never believed the advice
is not signiﬁcantly diﬀerent from that of all VN subjects (22.2% and 20.6%,
respectively; z = 1.066, p = 0.143).
These results suggest that providing advice is likely to increase sincere bids whensubjects believe them, and that providing advice makes subjects bid more sincerely—
not because subjects are inﬂuenced by the experimenter demand eﬀect, but because
subjects believe the advice.
We also observe that the same results as VA subjects hold for AA subjects.33 On theother hand, we ﬁnd that there is no statistical diﬀerence in the rate of sincere bidding

33

The number of AA subjects who chose (a) believed the advice before practice periods, (b) believed
the advice after practice periods but before real periods, (c) believed the advice during real periods,and (d) never believed were, respectively, 13, 6, 7, and 28. The AA subjects who believed the advice
bid signiﬁcantly more sincerely compared with those who never did (p < 0.001). The rate of sincere
bidding among the AA subjects who never believed the advice is not signiﬁcantly diﬀerent from thatof all AN subjects (p = 0.697).

Online Appendix – Page 9

between agents who believed and those who never did in PA (p = 0.210).34 Moreover,
the rate of sincere bidding among those who never believed the advice is signiﬁcantly
higher than the overall rate of sincere bidding in PN (p < 0.001).

34

The number of PA subjects who chose (a) believed the advice before practice periods, (b) believed
the advice after practice periods but before real periods, (c) believed the advice during real periods,and (d) never believed were, respectively, 3, 1, 0, and 65. That is, 4 subjects believed the advice, and65 never did.

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E

Additional table
Table 21: Bid category by treatments and units.
(a) Both units

Bid category
SincereOver
Under

Vickrey
Pay-your-bid
VA
VN
VA − VN
PA
PN
PA − PN
∗∗∗
0.469
0.206
0.263
0.083
0.058
0.025∗∗∗(0.499) (0.404)(0.276) (0.234)
∗∗∗
0.453
0.634 −0.181
0.006
0.009 −0.004∗∗(0.498) (0.482)(0.074) (0.095)
0.078
0.160 −0.083∗∗∗ 0.911
0.933 −0.021∗∗∗(0.268) (0.367)(0.284) (0.250)(b) Unit 1

Vickrey
Pay-your-bid
Bid category
VA
VN
VA − VN
PA
PN
PA − PN
0.416
0.175
0.241∗∗∗ 0.020
0.006
0.014∗∗∗
Sincere(0.493) (0.380)(0.141) (0.078)
0.556
0.732 −0.176∗∗∗ 0.001
0.001
0.000
Over
(0.497) (0.443)(0.034) (0.033)
0.029
0.093 −0.065∗∗∗ 0.979
0.993 −0.014∗∗∗Under(0.167) (0.291)(0.145) (0.085)(c) Unit 2

Bid category
SincereOver
Under

Vickrey
Pay-your-bid
VA
VN
VA − VN
PA
PN
PA − PN
∗∗∗
0.523
0.237
0.286
0.146
0.110
0.036∗∗∗(0.500) (0.425)(0.353) (0.313)
∗∗∗
0.350
0.536 −0.185
0.010
0.017 −0.007∗∗(0.477) (0.499)(0.099) (0.130)
∗∗∗
0.127
0.228 −0.101
0.844
0.873 −0.029∗∗∗(0.333) (0.419)(0.363) (0.333)

Notes: ∗ denotes signiﬁcant at the 10% level, ∗∗ at the 5% level, and ∗∗∗ at the 1% level. Numbers inparentheses are standard deviations.

Online Appendix – Page 11

F

Experimental instructions (VA and VN)

Note: In this experiment, please remember that you cannot communicate with othersubjects. If there is communication, this experiment will be stopped immediately.
First, please conﬁrm the following items. If any of the items are missing, pleasecontact the experimenter.
• Instructions (this handout)• Record sheet• Ballpoint pen, pencil, and eraser• Calculator

F.1

Overview

In this experiment, you will act as a bidder in a sequence of auctions. Three bidders
will participate in each auction. At the beginning of each period of the auction, theexperimenter randomly matches you with two persons from the other subjects. The
three of you will form a group. This experiment consists of 25 periods. The persons you
are matched with will change every period. You will not know who you are matchedwith either during or after the experiment.
The rewards you receive after the experiment are determined based on the decisions
you and the other two bidders make in the experiment. Your rewards will be paid toyou in cash at the end of the experiment. A more detailed explanation of your rewards
will be provided later in F.3. Rewards.

F.2

Auction

F.2.1

Procedure in each period

1. Two units of an identical object will be auctioned oﬀ in every period. Threebidders, including yourself, will participate in each period of the auction.
2. Each bidder will be assigned a value for the ﬁrst unit (“value for the ﬁrst unit”)
and another value for the second unit (“value for the second unit”). Your values
will be randomly drawn from the interval 0 JPY to 1,000 JPY with incrementsof 10 JPY. Any numerical value within this interval has an equal possibility of

Online Appendix – Page 12

being drawn and being assigned as your value. The higher of these two values
will be your “value for the ﬁrst unit,” while the lower value will be your “value
for the second unit.” Each of the other two bidders will be assigned values forthe two units in the same manner as mentioned above. The values assigned tothe other two bidders will typically be diﬀerent from yours. Please note that, foreach bidder, his/her value for the second unit will always be lower than his/her
for the ﬁrst unit. In addition, your “value for the ﬁrst unit” and “value for thesecond unit” are only for your private information. The other bidders will notknow your values.
3. You will submit your “bid for the ﬁrst unit” and “bid for the second unit” to theexperimenter. Then, please note the following three points:• Your “bid for the ﬁrst unit” must be higher than your “bid for the second
unit.”• Your bids must exceed 0 JPY.
• Your bids must be increments of 10 JPY.
4. Each of the three bidders will submit two bids. Therefore, there will be a total of
6 bids. The two highest bids will be the winning bids and a bidder who submits
the winning bid(s) will win the object(s). In the case of a tie among the bids,
the experimenter will randomly determine the winning bids. This procedure
determines the number of units each bidder will earn.
5. If a bidder wins one unit (or two units), his/her “earnings” are equal to his/hervalue for the ﬁrst unit (or the sum of his/her values for the ﬁrst and second units)less his/her payment. If a bidder does not win anything, his/her “earnings” are
0.
F.2.2

Earnings calculation

We explain how to calculate bidder’s earnings if the bidder wins an object using examples. There are three bidders, A, B, and C. Here, we focus on bidder A. In thefollowing examples, amounts are displayed in JPY.
(1) The case where a bidder wins one unit: A bidder who wins one unit will
pay the highest bid from among the other bidders’ losing bids.

Online Appendix – Page 13

Example F.1. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.
Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

600

450

B

500

300

C

400

250

Here, the winning bids are “A’s 600” and “B’s 500.” The losing bids are “A’s 450,”“B’s 300,” “C’s 400,” and “C’s 250.” Bidder A pays the highest bid from among theother bidders’ losing bids (400). This payment diﬀers from A’s own bid for the ﬁrst
unit. Then, bidder A earns the following amount:
680 (value for the ﬁrst unit) − 400 (payment) = 280
Example F.2. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.
Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

800

350

B

750

300

C

700

250

Here, the winning bids are “A’s 800” and “B’s 750.” Thus, bidder A wins one unit.
The losing bids are “A’s 350,” “B’s 300,” “C’s 700,” and “C’s 250.” Bidder A pays
the highest bid from among the other bidders’ losing bids (700). This payment diﬀers
from A’s own bid for the ﬁrst unit. Then, bidder A earns the following amount:
680 (value for the ﬁrst unit) − 700 (payment) = −20(2) The case where a bidder wins two units: A bidder who wins two units will
pay the sum of the highest and second-highest bids from among the other bidders’losing bids.
Example F.3. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.

Online Appendix – Page 14

Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

600

550

B

500

300

C

400

250

Here, the winning bids are “A’s 600” and “A’s 550.” The losing bids are “B’s500,” “B’s 300,” “C’s 400,” and “C’s 250.” Bidder A pays the sum of the highest andsecond-highest bids from among the other bidders’ losing bids (400 + 500 = 900). This
payment diﬀers from A’s own bids. Then, bidder A earns the following amount:
680 (value for the ﬁrst unit) + 480 (value for the second unit) − 900 (payment) = 260
Example F.4. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.

Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

900

850

B

800

600

C

700

550

Here, the winning bids are “A’s 900” and “A’s 850.” The losing bids are “B’s800,” “B’s 600,” “C’s 700,” and “C’s 550.” Bidder A pays the sum of the highest andsecond-highest bids from among the other bidders’ losing bids (800+700 = 1500). This
payment diﬀers from A’s own bids. Then, bidder A earns the following amount:
680 (value for the ﬁrst unit)+480 (value for the second unit)−1500 (payment) = −340
The following summarizes how to calculate your earnings:• The case where you win one unit, and the third-highest bid is yours:Your earnings = your value for the ﬁrst unit − fourth highest bid• The case where you win one unit, and the third-highest bid is not yours:Your earnings = your value for the ﬁrst unit − third highest bid

Online Appendix – Page 15

Note that when your payment is higher than your value for the ﬁrst unit, yourearnings will be negative.
• The case where you win two units:Your earnings = (your value for the ﬁrst unit + your value for the second unit)− (third highest bid + fourth highest bid)
Note that when your payment is higher than the sum of your values for the ﬁrst
and second units, your earnings will be negative.
• If you do not win anything, your earnings are 0.

F.3

Rewards

Here, we explain the rewards you receive after the experiment. Your rewards are thesum of your earnings over all 25 periods and a participation fee of 1,000 JPY plus youscore in the quiz to check your understanding of each instruction.
For example, if the sum of your earnings is 2,580 JPY and your score on the quizis 420, your rewards will be 4,000 JPY.

Online Appendix – Page 16

Online Appendix – Page 17

12

11

10

9

8

7

6

5

4

3

2

1

PeriodValue for theﬁrst unit

Value for thesecond unit

Bid for theﬁrst unit

Bid for thesecond unit

Recording Sheet
Payment(ﬁrst unit)

Payment(second unit)

Seat Number
Payment(total)Yourearnings

Online Appendix – Page 18

25

24

23

22

21

20

19

18

17

16

15

14

13

PeriodValue for theﬁrst unit

Value for thesecond unit

Bid for theﬁrst unit

Bid for thesecond unit

Recording Sheet
Payment(ﬁrst unit)

Payment(second unit)

Seat Number
Payment(total)Yourearnings

G

Experimental instructions (PA and PN)

Note: In this experiment, please remember that you cannot communicate with othersubjects. If there is communication, this experiment will be stopped immediately.
First, please conﬁrm the following items. If any of the items are missing, pleasecontact the experimenter.
• Instructions (this handout)• Record sheet• Ballpoint pen, pencil, and eraser• Calculator

G.1

Overview

In this experiment, you will act as a bidder in a sequence of auctions. Three bidders
will participate in each auction. At the beginning of each period of the auction, theexperimenter randomly matches you with two persons from the other subjects. The
three of you will form a group. This experiment consists of 25 periods. The persons you
are matched with will change every period. You will not know who you are matchedwith either during or after the experiment.
The rewards you receive after the experiment are determined based on the decisions
you and the other two bidders make in the experiment. Your rewards will be paid toyou in cash at the end of the experiment. A more detailed explanation of your rewards
will be provided later in G.3. Rewards.

G.2

Auction

G.2.1

Procedure in each period

1. Two units of an identical object will be auctioned oﬀ in every period. Threebidders, including yourself, will participate in each period of the auction.
2. Each bidder will be assigned a value for the ﬁrst unit (“value for the ﬁrst unit”)
and another value for the second unit (“value for the second unit”). Your values
will be randomly drawn from the interval 0 JPY to 1,000 JPY with incrementsof 10 JPY. Any numerical value within this interval has an equal possibility of

Online Appendix – Page 19

being drawn and being assigned as your value. The higher of these two values
will be your “value for the ﬁrst unit,” while the lower value will be your “value
for the second unit.” Each of the other two bidders will be assigned values forthe two units in the same manner as mentioned above. The values assigned tothe other two bidders will typically be diﬀerent from yours. Please note that, foreach bidder, his/her value for the second unit will always be lower than his/her
for the ﬁrst unit. In addition, your “value for the ﬁrst unit” and “value for thesecond unit” are only for your private information. The other bidders will notknow your values.
3. You will submit your “bid for the ﬁrst unit” and “bid for the second unit” to theexperimenter. Then, please note the following three points:• Your “bid for the ﬁrst unit” must be higher than your “bid for the second
unit.”• Your bids must exceed 0 JPY.
• Your bids must be increments of 10 JPY.
4. Each of the three bidders will submit two bids. Therefore, there will be a total of
6 bids. The two highest bids will be the winning bids and a bidder who submits
the winning bid(s) will win the object(s). In the case of a tie among the bids,
the experimenter will randomly determine the winning bids. This procedure
determines the number of units each bidder will earn.
5. If a bidder wins one unit (or two units), his/her “earnings” are equal to his/hervalue for the ﬁrst unit (or the sum of his/her values for the ﬁrst and second units)less his/her payment. If a bidder does not win anything, his/her “earnings” are
0.
G.2.2

Earnings calculation

We explain how to calculate bidder’s earnings if the bidder wins an object using examples. There are three bidders, A, B, and C. Here, we focus on bidder A. In thefollowing examples, amounts are displayed in JPY.
(1) The case where a bidder wins one unit: A bidder who wins one unit will
pay his/her bid for the ﬁrst unit.

Online Appendix – Page 20

Example G.1. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.
Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

600

450

B

500

300

C

400

250

Here, the winning bids are “A’s 600” and “B’s 500.” Bidder A pays his/her bid forthe ﬁrst unit (600). Then, bidder A earns the following amount:
680 (value for the ﬁrst unit) − 600 (payment) = 80
Example G.2. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.
Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

800

350

B

750

300

C

700

250

Here, the winning bids are “A’s 800” and “B’s 750.” Thus, bidder A wins one
unit and pays his/her bid for the ﬁrst unit (800). Then, bidder A earns the following
amount:680 (value for the ﬁrst unit) − 800 (payment) = −120
(2) The case where a bidder wins two units: A bidder who wins two units will
pay the sum of his/her bids.
Example G.3. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.
Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

600

550

B

500

300

C

400

250

Online Appendix – Page 21

Here, the winning bids are “A’s 600” and “A’s 550.” Bidder A pays the sum of
his/her bids (600 + 550 = 1150). Then, bidder A earns the following amount:
680 (value for the ﬁrst unit) + 480 (value for the second unit) − 1150 (payment) = 10
Example G.4. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bids from the three bidders.

Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

900

850

B

800

600

C

700

550

Here, the winning bids are “A’s 900” and “A’s 850.” Bidder A pays the sum of
his/her bids (900 + 850 = 1750). Then, bidder A earns the following amount:
680 (value for the ﬁrst unit)+480 (value for the second unit)−1750 (payment) = −590
The following summarizes how to calculate your earnings:• The case where you win one unit:
Your earnings = your value for the ﬁrst unit − your bid for the ﬁrst unit
Note that when your payment is higher than your value for the ﬁrst unit, yourearnings will be negative.
• The case where you win two units:Your earnings = (your value for the ﬁrst unit + your value for the second unit)− (your bid for the ﬁrst unit + your bid for the second unit)
Note that when your payment is higher than the sum of your values for the ﬁrst
and second units, your earnings will be negative.
• If you do not win anything, your earnings are 0.

Online Appendix – Page 22

G.3

Rewards

Here, we explain the rewards you receive after the experiment. Your rewards are thesum of your earnings over all 25 periods and a participation fee of 1,000 JPY plus youscore in the quiz to check your understanding of each instruction.
For example, if the sum of your earnings is 2,580 JPY and your score on the quizis 420, your rewards will be 4,000 JPY.

Online Appendix – Page 23

Online Appendix – Page 24

12

11

10

9

8

7

6

5

4

3

2

1

PeriodValue for theﬁrst unit

Value for thesecond unit

Bid for theﬁrst unit

Bid for thesecond unit

Recording Sheet
Payment(ﬁrst unit)

Payment(second unit)

Seat Number
Payment(total)Yourearnings

Online Appendix – Page 25

25

24

23

22

21

20

19

18

17

16

15

14

13

PeriodValue for theﬁrst unit

Value for thesecond unit

Bid for theﬁrst unit

Bid for thesecond unit

Recording Sheet
Payment(ﬁrst unit)

Payment(second unit)

Seat Number
Payment(total)Yourearnings

H

Text of advice (VA and PA)

Advice on decision making
The following advice is about the auction in which you are participating. Please consider carefully whether this advice is true or false. It is completely up to you whether
you follow the advice or not.
You can maximize your earnings by bidding your valuations as they are, regardless ofwhat others bid.

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I

Auction screens and procedures (VA, VN, PA, and
PN)

I.1

Bidding screen

When you are ready to submit your bid, the following screen will be displayed. The
upper-left corner of the screen displays the current experimental period. The screenshot
below shows that the current experimental period is the ﬁrst period in a total of 25
periods. In the center of the screen, “Your value for the ﬁrst unit” and “Your value
for the second unit” will be displayed. First, transcribe this information into thecorresponding columns on the record sheet.
Next, you submit “Your bid for the ﬁrst unit” and “Your bid for the second unit,”
both in increments of 10 JPY. You input your bids into the corresponding cells on thescreen. Please note that your bid for the ﬁrst unit must be higher than your bid for thesecond unit. After that, transcribe your bids into the corresponding columns on therecord sheet. After the transcription, click the “OK” button.
You will have 60 seconds to ﬁnalize your bid on this screen.

Online Appendix – Page 27

I.2

Auction results screen

After all the subjects have clicked the “OK” button, the following screen will be displayed. On the left side of the screen, all the bids will be ranked from highest to
lowest. The right side will be divided into three sections. The top section will show
“Your bid for the ﬁrst unit,” “Your bid for the second unit,” and the number of units
you win in this auction. In the middle section, your payments will be displayed in thefollowing order: your payment for the ﬁrst unit, your payment for the ﬁrst unit, andyour total payment in this auction. Transcribe this information into the corresponding
columns on your record sheet. Finally, the bottom section will show the amount of“Your earnings from this auction.” Transcribe this information into the corresponding
column on your record sheet. After the transcription, click the “Next” button.

After all the subjects have clicked the “Next” button, the next auction will start.
This marks the end of one auction period. This experiment includes a series of 25
auctions.

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J

Quiz (VA, VN, PA, and PN)

Please answer all questions below.
The bids from three bidders are shown in the following table. Suppose that B’svalue for the ﬁrst unit is 900, and B’s value for the second unit is 700. Suppose thatC’s value for the ﬁrst unit is 500.
Bidder

Bid for the ﬁrst unit

Bid for the second unit

A

800

500

B

1000

700

C

600

500

(1) Find (two) winning bids.
(2) Calculate B’s payment.
(3) Calculate B’s earnings.
(4) Calculate C’s payment.
(5) Calculate C’s earnings.
Suppose that B’s bid for the ﬁrst unit is 900; all other bids are shown in the table
above.
(6) Find (two) winning bids.
(7) Calculate B’s payment.
(8) Calculate B’s earnings.
Suppose that B’s bid for the ﬁrst unit is 400 and 300 for the second unit; all other bids
are shown in the table above.
(9) Find (two) winning bids.
(10) Calculate B’s payment.
(11) Calculate B’s earnings.

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Suppose that C’s bid for the ﬁrst unit is 1,000; all other bids are shown in the table
above.
(12) Find (two) winning bids.
(13) Calculate C’s payment.
(14) Calculate C’s earnings.
Suppose that C’s bid for the ﬁrst unit is 500; all other bids are shown in the table
above.
(15) Find (two) winning bids.
(16) Calculate C’s payment.
(17) Calculate C’s earnings.

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K

Post-experiment survey (VA and PA)
Seat Number
Faculty / Department

Age

Gender: Male / Female

1. Did you understand the auction rules (that is, how to calculate bidder’s earnings)?
(a) I understood it after receiving the instructions.
(b) I understood it after conﬁrming the rules.
(c) I understood it by following the practice, and before the ﬁrst real period.
(d) I understood it during the real periods. (from period)(e) I did not understand it.
2. Did you trust the decision-making advice?
(a) I trusted it before the practice.
(b) I trusted it after the practice, and before the ﬁrst real period.
(c) I began trusting it during the real periods. (from period)(d) I did not trust it.
If you answer is (c) or (d), please write your reason(s) below.

3. How did you decide to bid? Please write speciﬁcally.
The number of times you bid your values: ﬁrst unit (times), second unit (times).

4. What did you think about others’ bids? Please circle your selection and write
speciﬁc details.

Online Appendix – Page 31

(Thought deeply, Didn’t think much, Didn’t think at all)

5. What do you think is the optimal bidding strategy? Please write your ideas andtheir reasoning.

6. If you had been aware of the others’ values, would you have changed the way you
decided to bid? If so, how would it have changed? Please write your ideas andreasons.

Thank you for your answers.

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L

Post-experiment survey (VN and PN)
Seat Number
Faculty / Department

Age

Gender: Male / Female

1. Did you understand the auction rules (that is, how to calculate bidder’s earnings)?
(a) I understood it after receiving the instructions.
(b) I understood it after conﬁrming the rules.
(c) I understood it by following the practice, and before the ﬁrst real period.
(d) I understood it during the real periods. (from period)(e) I did not understand it.
2. How did you decide to bid? Please write speciﬁcally.
The number of times you bid your values: ﬁrst unit (times), second unit (times).

3. What did you think about others’ bids? Please circle your selection and write
speciﬁc details.
(Thought deeply, Didn’t think much, Didn’t think at all)

4. What do you think is the optimal bidding strategy? Please write your ideas andtheir reasoning.

Online Appendix – Page 33

5. If you had been aware of the others’ values, would you have changed the way you
decided to bid? If so, how would it have changed? Please write your ideas andreasons.

Thank you for your answers.

Online Appendix – Page 34

M

Experimental instruction (AA and AN)

Note: In this experiment, please remember that you cannot communicate with othersubjects. If there is communication, this experiment will be stopped immediately.
First, please conﬁrm the following items. If any of the items are missing, pleasecontact the experimenter.
• Instructions (this handout)• Record sheet• Ballpoint pen, pencil, and eraser• Calculator

M.1

Overview

In this experiment, you will act as a bidder in a sequence of auctions. Three bidders
will participate in each auction. At the beginning of each period of the auction, theexperimenter randomly matches you with two persons from the other subjects. The
three of you will form a group. This experiment consists of 25 periods. The persons you
are matched with will change every period. You will not know who you are matchedwith either during or after the experiment.
The rewards you receive after the experiment are determined based on the decisions
you and the other two bidders make in the experiment. Your rewards will be paid toyou in cash at the end of the experiment. A more detailed explanation of your rewards
will be provided later in M.3. Rewards.

M.2

Auction

M.2.1

Procedure in each period

1. Two units of an identical object will be auctioned oﬀ in every period. Threebidders, including yourself, will participate in each period of the auction.
2. Each bidder will be assigned a value for the ﬁrst unit (“value for the ﬁrst unit”)
and another value for the second unit (“value for the second unit”). Your values
will be randomly drawn from the interval 0 JPY to 1,000 JPY with incrementsof 10 JPY. Any numerical value within this interval has an equal possibility of

Online Appendix – Page 35

being drawn and being assigned as your value. The higher of these two values
will be your “value for the ﬁrst unit,” while the lower value will be your “value
for the second unit.” Each of the other two bidders will be assigned values forthe two units in the same manner as mentioned above. The values assigned tothe other two bidders will typically be diﬀerent from yours. Please note that, foreach bidder, his/her second unit’s value will always be lower than his/her ﬁrst
unit’s value. In addition, your “value for the ﬁrst unit” and “value for the second
unit” are only for your private information. The other bidders will not know yourvalues.
3. In the auction, a price will start from 0 (initial price) and rise in increments of
10 JPY every 2 seconds. For each price, you are supposed to reveal your demand(i.e., units you wish to buy) at that price. Your demand starts from two units atprice 0, and you decide whether to reduce your demand as the price increases. As
will be explained later, the “demand reduction button” (hereinafter “button”) isdisplayed on your screen. To reduce your demand by one unit at a price, click
the button once. To reduce another unit, click the button again. Thus, clicking
the button twice makes your demand 0 units.
4. At the initial price, each of the three bidders demands two units; thus, the “aggregate demand” is six units. As the price increases, the aggregate demanddecreases. When the aggregate demand becomes two units, the auction is closed.
That is, the auction ends when the button is clicked four times or the auction
ends when the price reaches 2,000 JPY (i.e., the maximum limit price) even if
the aggregate demand does not become two units.
5. The two units will be allocated to the remaining demands after the auction isclosed. We explain the number of units you win, and your payments in each of
the four cases below:a) The case where your demand becomes 0 units (i.e., you click the button
twice) during the auction:
You win 0 units, and you pay 0.
b) The case where your demand is one unit (i.e., you click the button once)
when the aggregate demand becomes three units:
The auction is closed when someone clicks the button once after that time.
(1) If your click closes the auction, then you win 0 units, and you pay 0.

Online Appendix – Page 36

(2) If some other bidder’s click closes the auction, then you win one unit,
and you pay the closing price.
c) The case where your demand remains two units (i.e., you never clicked the
button) until the aggregate demand becomes three units:
You are assured to earn at least one unit. You pay the price for this unit
when you are assured. The auction is closed when someone clicks the button
once after that time.
(1) If your click closes the auction, then you win one unit, and you pay theprice when you are assured.
(2) If some other bidder’s click closes the auction, then you win two units,
and you pay the price when you are assured the ﬁrst unit + the closing
price.
d) The case where the price reaches 2,000 JPY before the aggregate demand
becomes two units:
Each unsold unit will be allocated with equal probabilities to the remaining
demands.
(1) If no bidder is assured to win one unit until the auction is closed, twounits will be allocated to remaining demands with equal probabilities.
You pay 2,000 JPY for each unit you win. That is, you pay:“the number of units you win (0, 1, or 2)” × 2,000 JPY.
(2) If some bidder is assured to win one unit until the auction is closed,
the remaining one unit will be allocated to the remaining demands withequal probabilities. If you win one unit at the end of the auction, its
price is 2,000 JPY. If you have been assured to win one unit once theprice reaches 2,000 JPY, then you also pay the price when you wereassured one unit. Thus, if you have been assured no unit, you pay:“the number of units you win (0 or 1)” × 2,000 JPY.
If you have been assured one unit during the auction, you pay:“the price when you were assured” + “the number of units you win (0,1, or 2)” × 2,000 JPY.
M.2.2

Earnings calculation

We explain how to calculate bidder’s earnings if the bidder wins some units using theseexamples. There are three bidders, A, B, and C. Here, we focus on bidder A. In theOnline Appendix – Page 37

following examples, amounts are displayed in JPY. The price at the time a bidder
intends to click the button is called the “demand reduction price.” Now, consider thecase where the button is clicked four times before the price reaches the maximum limit
price.
(1) Bidder demanding one unit when the auction is closed
Example M.1. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the “demand reduction prices” (the prices atwhich bidders plan to click the button). All the prices in the table will not be observed
during the auction as the auction is closed before the button is clicked for all the prices.

BidderFirst demand reduction priceSecond demand reduction price

A

450

600

B

300

500

C

250

400

“C’s 250,” “B’s 300,” “C’s 400,” and “A’s 450” are the four lowest (demand reduction) prices in ascending order. When bidder A clicks the button at the forth lowest
price (450), the auction ends. As A’s own click closes the auction and A’s demand is
one unit at that time, A’s payment is the third lowest price (400). This payment is
diﬀerent from A’s own demand reduction price. Then, bidder A earns the following
amount:680 (value for the ﬁrst unit) − 400 (payment) = 280
Example M.2. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bidders’ demand reduction prices.

BidderFirst demand reduction priceSecond demand reduction price

A

350

800

B

300

750

C

250

700

“C’s 250,” “B’s 300,” “A’s 350,” and “C’s 700” are the four lowest (demand reduction) prices in ascending order. When bidder C clicks the button at the fourth lowest
price (700), the auction ends. As C’s click closes the auction and A’s demand is one

Online Appendix – Page 38

unit at that time, A’s payment is 700. This payment is diﬀerent from A’s own demand
reduction price. Then, bidder A earns the following amount:
680 (value for the ﬁrst unit) − 700 (payment) = −20(2) Bidder demanding two units when the auction is closed
Example M.3. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bidders’ demand reduction prices.
BidderFirst demand reduction priceSecond demand reduction price

A

550

600

B

300

500

C

250

400

“C’s 250,” “B’s 300,” “C’s 400,” and “B’s 500” are the four lowest (demand reduction) prices in ascending order. When bidder C clicks the button at the third lowest
price (400), A is assured to win one unit. Subsequently, when B clicks the button at
the forth lowest price (500), the auction ends. Thus, A’s payment is the sum of thethird and fourth lowest prices (400 + 500 = 900). Then, bidder A earns the following
amount:680 (value for the ﬁrst unit) + 480 (value for the second unit) − 900 (payment) = 260
Example M.4. Suppose A’s values for the ﬁrst and second units are 680 and 480,
respectively. The table below displays the bidders’ demand reduction prices.
BidderFirst demand reduction priceSecond demand reduction price

A

850

900

B

600

800

C

550

700

“C’s 550,” “B’s 600,” “C’s 700,” and “B’s 800” are the four lowest (demand reduction) prices in ascending order. A’s payment is calculated similarly to Example M.3.
and is the sum of the third and fourth lowest prices (700 + 800 = 1500). Thus, bidder
A earns the following amount:
680 (value for the ﬁrst unit)+480 (value for the second unit)−1500 (payment) = −340

Online Appendix – Page 39

When the button is clicked four times before the price reaches the maximum limit
price, the following summarizes how to calculate your earnings:• The case where your demand is 0 units at the end of the auction:
Your earnings = 0• The case where your demand is one unit at the end of the auction:◦ If some other bidder’s click closes the auction, then:Your earnings = your value for the ﬁrst unit−fourth demand reduction price◦ If your click closes the auction, then:Your earnings = your value for the ﬁrst unit−third demand reduction price• The case where your demand remains two units at the end of the auction:
Your earnings = (your value for the ﬁrst unit + your value for the second unit)− (third demand reduction price + fourth demand reduction price)
If the button is not clicked four times before the price reaches the maximum limit
price, then your earnings are the sum of values for the units you win minus the payment
calculated as described in 5d of Section M.2.1. If you do not win anything, your earnings
are 0.

M.3

Rewards

Here, we explain the rewards you receive after the experiment. Your rewards are thesum of your earnings over all 25 periods and a participation fee of 1,000 JPY plus youscore in the quiz to check your understanding of each instruction.
For example, if the sum of your earnings is 2,580 JPY and your score on the quizis 420, your rewards will be 4,000 JPY.

Online Appendix – Page 40

Online Appendix – Page 41

Value for thesecond unit

First demand
reduction priceSecond demand
reduction price

Payment(ﬁrst unit)

Payment(second unit)

Seat Number
Payment(total)Yourearnings

Note: If you reduced demand once or did not reduce at all, please denote a slash mark in the corresponding cells.

12

11

10

9

8

7

6

5

4

3

2

1

PeriodValue for theﬁrst unit

Recording SheetOnline Appendix – Page 42

Value for thesecond unit

First demand
reduction priceSecond demand
reduction price

Payment(ﬁrst unit)

Payment(second unit)

Seat Number
Payment(total)Yourearnings

Note: If you reduced demand once or did not reduce at all, please denote a slash mark in the corresponding cells.

25

24

23

22

21

20

19

18

17

16

15

14

13

PeriodValue for theﬁrst unit

Recording SheetN

Text of advice (AA)

Advice on decision making
The following advice is about the auction in which you are participating. Please consider carefully whether this advice is true or false. It is completely up to you whether
you follow the advice or not.
You can maximize your earnings by reducing your demands at your values as they are,regardless of the prices at which others reduce their demands.

Online Appendix – Page 43

O

Auction screens and procedures (AA and AN)

O.1

Screen before beginning the auction

At the beginning of each period of the auction, the following screen will be displayed.
The upper-left corner of the screen displays the current experimental period. The
screenshot below shows that the current experimental period is the ﬁrst period in a
total of 25 periods. In the center of the screen, “Your value for the ﬁrst unit” and“Your value for the second unit” will be displayed. First, transcribe this informationin the corresponding columns on the record sheet.

O.2

Decision-making screen

When an auction starts, the following screen will be displayed. The upper-left cornerof the screen displays the current experimental period. The screenshot below showsthat the current experimental period is the ﬁrst period in a total of 25 periods.
In the center of the screen, “Your value for the ﬁrst unit” and “Your value for thesecond unit” will be displayed. In the box immediately below, you will see the current
price. The price will rise in increments of 10 JPY every 2 seconds.
On the left of the screen, each bidder’s demand at the current price will be displayed.
The screenshot below indicates that each bidder’s demand is 2 as the auction has juststarted. Please note that the other bidders’ numbers “1” and “2” will be randomly

Online Appendix – Page 44

assigned after determining the group members. Hence, you cannot identify who they
are based on these numbers.
On the right of the screen, you will see an event table. This table shows the history,
from the beginning to the present point in time, of which bidders have reduced demand
and at what price, and whether they have been assured to win one unit and at what
price.
At the bottom of the screen, you can see the “demand reduction button.” If you
click this button once, you can reduce your demand by one unit. Since your demandis 2 at the beginning of the auction, you can click the button at most two times.
1) Screen just after the auction has begun

Online Appendix – Page 45

2) Screen in case you are assured to win one unit

3) Screen in case you are assured to win one more unit

Online Appendix – Page 46

When one period of the auction ends, transcribe your demand reduction price (atmost two) in the corresponding cells on the record sheet. If the number of times you
have reduced your demand is either 1 or 0, cross out the blank areas in the corresponding cells on the record sheet with a diagonal line. After the transcription, click the “Goto the conﬁrmation screen” button.

O.3

Conﬁrmation screen

When all the subjects have ﬁnished their inputs, the following screen will be displayed.
On the left side of the screen, the event table is displayed again. The right side shows
information on your earnings. From the top to the bottom, “‘Your value for the ﬁrst
unit,” “Your value for the second unit,” the number of units you have earned in thisauction, your total payment in this auction, and “Your earnings from this auction” will
be displayed. Transcribe your payment for the ﬁrst unit, your payment for the second
unit, and your total payment into the corresponding columns on your record sheet. If
the payment is 0, transcribe 0 into the corresponding cells on your record sheet. Afterthe transcription, click the “OK” button.

After all the bidders have clicked the “OK” button, the next period of the auction
will begin. This marks the end of one auction period. This experiment involves a seriesof 25 auctions.

Online Appendix – Page 47

P

Quiz (AA and AN)

Please answer all the questions below:
The three bidders planning demand reduction of the prices are shown in the following table. Suppose that B’s value for the ﬁrst unit is 900, and B’s value for the second
unit is 700. Suppose that C’s value for the ﬁrst unit is 500.
BidderFirst demand reduction priceSecond demand reduction price

A

500

800

B

700

1000

C

500

600

(1) Specify winning bidders and how many unit(s) each winning bidder wins.
(2) Calculate B’s payment.
(3) Calculate B’s earnings.
(4) Calculate C’s payment.
(5) Calculate C’s earnings.
Suppose that B’s second demand reduction price is 900; all other demand reduction
prices are the same as the table above.
(6) Specify winning bidders and how many unit(s) each bidder has won.
(7) Calculate B’s payment.
(8) Calculate B’s earnings.
Suppose that B’s ﬁrst and second demand reduction prices are 300 and 400, respectively; all other demand reduction prices are the same as the table above.
(9) Specify winning bidders and how many unit(s) each bidder has won.
(10) Calculate B’s payment.
(11) Calculate B’s earnings.

Online Appendix – Page 48

Suppose that C’s second demand reduction price is 1,000; all other demand reduction
prices are the same as the table above.
(12) Specify winning bidders and how many unit(s) each bidder has won.
(13) Calculate C’s payment.
(14) Calculate C’s earnings.
Suppose that C’s second demand reduction price is 500; all other demand reduction
prices are the same as the table above.
(15) Specify winning bidders and how many unit(s) each bidder has won.
(16) Calculate C’s payment.
(17) Calculate C’s earnings.

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Q

Post-experiment survey (AA)Seat Number
Faculty / Department

Age

Gender: Male / Female

1. Did you understand the auction rules (that is, how to calculate bidder’s earnings)?
(a) I understood it after receiving the instructions.
(b) I understood it after conﬁrming the rules.
(c) I understood it by following the practice, and before the ﬁrst real period.
(d) I understood it during the real periods. (from period)(e) I did not understand it.
2. Did you trust the decision-making advice?
(a) I trusted it before the practice.
(b) I trusted it after the practice, and before the ﬁrst real period.
(c) I began trusting it during the real periods. (from period)(d) I did not trust it.
If you answer is (c) or (d), please write your reason(s) below.

3. How did you decide to reduce your demands? Please write speciﬁcally.
The number of times you reduce your demands at your values : ﬁrst unit (unit (

times), second

times).

4. What did you think about others’ demand reductions? Please circle your selection
and write speciﬁc details.

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(Thought deeply, Didn’t think much, Didn’t think at all)

5. What do you think is the optimal demand reduction strategy? Please write yourideas and their reasoning.

6. If you had been aware of the others’ values, would you have changed the way you
decided to reduce your demands? If so, how would it have changed? Please write
your ideas and reasons.

Thank you for your answers.

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R

Post-experiment survey (AN)Seat Number
Faculty / Department

Age

Gender: Male / Female

1. Did you understand the auction rules (that is, how to calculate bidder’s earnings)?
(a) I understood it after receiving the instructions.
(b) I understood it after conﬁrming the rules.
(c) I understood it by following the practice, and before the ﬁrst real period.
(d) I understood it during the real periods. (from period)(e) I did not understand it.
2. How did you decide to reduce your demands? Please write speciﬁcally.
The number of times you reduce your demands at your values : ﬁrst unit (unit (

times), second

times).

3. What did you think about others’ demand reductions? Please circle your selection
and write speciﬁc details.
(Thought deeply, Didn’t think much, Didn’t think at all)

4. What do you think is the optimal demand reduction strategy? Please write yourideas and their reasoning.

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5. If you had been aware of the others’ values, would you have changed the way you
decided to reduce your demands? If so, how would it have changed? Please write
your ideas and reasons.

Thank you for your answers.

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S

Individual bidding data

This section provides ﬁgures showing that each subject’s bidding behavior in eachtreatment.
Legends on the ﬁgures• x-axis: period• y-axis: bid value• Green line with ◦: quiz score = 17
• Orange line with ×: quiz score < 17
• Blue dotted line: positive payoﬀ• Red solid line: negative payoﬀ

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Figure 6: Time evolution of the gap between bid and value for unit 1 in VA1.

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Figure 7: Time evolution of the gap between bid and value for unit 2 in VA1.

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Figure 8: Time evolution of the gap between bid and value for unit 1 in VA2.

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Figure 9: Time evolution of the gap between bid and value for unit 2 in VA2.

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Figure 10: Time evolution of the gap between bid and value for unit 1 in VA3.

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Figure 11: Time evolution of the gap between bid and value for unit 2 in VA3.

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Figure 12: Time evolution of the gap between bid and value for unit 1 in VN1.

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Figure 13: Time evolution of the gap between bid and value for unit 2 in VN1.

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Figure 14: Time evolution of the gap between bid and value for unit 1 in VN2.

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Figure 15: Time evolution of the gap between bid and value for unit 2 in VN2.

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Figure 16: Time evolution of the gap between bid and value for unit 1 in PA1.

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Figure 17: Time evolution of the gap between bid and value for unit 2 in PA1.

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Figure 18: Time evolution of the gap between bid and value for unit 1 in PA2.

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Figure 19: Time evolution of the gap between bid and value for unit 2 in PA2.

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Figure 20: Time evolution of the gap between bid and value for unit 1 in PA3.

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Figure 21: Time evolution of the gap between bid and value for unit 2 in PA3.

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Figure 22: Time evolution of the gap between bid and value for unit 1 in PN1.

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Figure 23: Time evolution of the gap between bid and value for unit 2 in PN1.

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Figure 24: Time evolution of the gap between bid and value for unit 1 in PN2.

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Figure 25: Time evolution of the gap between bid and value for unit 2 in PN2.

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Figure 26: Time evolution of the gap between bid and value for unit 1 in PN3.

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Figure 27: Time evolution of the gap between bid and value for unit 2 in PN3.

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Figure 28: Time evolution of the gap between bid and value for unit 1 in AA1.

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Figure 29: Time evolution of the gap between bid and value for unit 2 in AA1.

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Figure 30: Time evolution of the gap between bid and value for unit 1 in AA2.

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Figure 31: Time evolution of the gap between bid and value for unit 2 in AA2.

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Figure 32: Time evolution of the gap between bid and value for unit 1 in AA3.

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Figure 33: Time evolution of the gap between bid and value for unit 2 in AA3.

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Figure 34: Time evolution of the gap between bid and value for unit 1 in AN1.

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Figure 35: Time evolution of the gap between bid and value for unit 2 in AN1.

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Figure 36: Time evolution of the gap between bid and value for unit 1 in AN2.

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Figure 37: Time evolution of the gap between bid and value for unit 2 in AN2.

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Figure 38: Time evolution of the gap between bid and value for unit 1 in AN3.

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Figure 39: Time evolution of the gap between bid and value for unit 2 in AN3.

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References
Jacquemet, N. and O. L’Haridon (2018) Experimental Economics: Method and Applications, Cambridge University Press.

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