On the relative importance of the hot stove effect and the tendency to rely on small samples

Judgment and Decision Making, Vol. 4, No. 5, August 2009, pp. 429–435
On the relative importance of the hot stove effect and the tendency
to rely on small samples
Takemi Fujikawa?
Centre for Policy Research and International Studies
Universiti Sains Malaysia
Abstract
Experiments have suggested that decisions from experience differ from decisions from description. In experience-
based decisions, the decision makers often fail to maximise their payoffs. Previous authors have ascribed the effect of
underweighting of rare outcomes to this deviation from maximisation. In this paper, I re-examine and provide further
analysis on the effect with an experiment that involves a series of simple binary choice gambles. In the current exper-
iment, decisions that bear small consequences are repeated hundreds of times, feedback on the consequence of each
decision is provided immediately, and decision outcomes are accumulated. The participants have to learn about the out-
come distributions through sampling, as they are not explicitly provided with prior information on the payoff structure.
The current results suggest that the “hot stove effect” is stronger than suggested by previous research and is as important
as the payoff variability effect and the effect of underweighting of rare outcomes in analysing decisions from experience
in which the features of gambles must be learned through a sampling process.
Keywords: decisions from experience, payoff variability, rare events, uncertainty, undersampling.
1 Introduction
mental problem of learning that reduces the DMs’ likeli-
hood of repeating decisions that got them in trouble. The
Much attention has been given to the distinction between
hot stove effect implies a bias against a risky alternative
decisions from description and decisions from experi-
in binary experience-based decisions (Denrell & March,
ence. In experience-based decisions, people experience
2001). The bias is a product of the tendency to reproduce
dif?culty in estimating and understanding uncertainty.
actions that have been successful and avoid recent actions
Erev and Barron (2005) hypothesised that two main be-
that have led to poor outcomes.
havioural tendencies determine the effect of rare events
on repeated decisions from experience. The ?rst is a ten-
Previous research on experience-based decisions has
dency to rely on small samples of past experiences (also
led to mixed conclusions with regard to the descriptive
proposed by Fox & Hadar, 2006). This tendency leads to
value of the hot stove effect. Whereas some studies
underweighting of rare events, as most samples are not
(e.g., Denrell & March, 2001) demonstrate its impor-
likely to include the rare events. The second is a ten-
tance, other studies (e.g., Barron & Erev, 2003; Erev &
dency to rely on recent experiences. When the informa-
Barron, 2005) suggest that this effect is weak. In this
tion available to the decision makers (DMs) is limited to
paper, I try to clarify this picture by focusing on choice
the obtained payoffs, this tendency leads to the “hot stove
problems in Barron and Erev (2003) and Erev and Bar-
effect”, which implies overweighting of the worst out-
ron (2005). The authors conducted experiments in which
comes. The hot stove effect was ?rst introduced by Mark
three choice problems (Problem 1, 2 and 3) were per-
Twain with his observation that if a cat jumped on a hot
formed by the participants, each involving 400-fold bi-
stove, then she would never jump on a hot stove again.
nary choice between H (an alternative with higher ex-
However, the cat would never jump even on a cold stove.
pected value) and L (an alternative with lower expected
Coutu (2006) states that the hot stove effect is a funda-
value). Table 1 shows the payoff structure of each prob-
lem. For example, one selection of H in Problem 1 made
?I thank Hidenori Oda for his helpful comments and valuable re-
the participants earn four points with probability 0.8 and
search support. I gratefully acknowledge the valuable suggestions and
zero point otherwise. The participants in their study were
comments of Jon Baron, Greg Barron, Ido Erev, Nick Feltovich and two
told that the experiments included many trials, and their
anonymous reviewers. All errors remain my own. Address: Takemi Fu-
jikawa, Centre for Policy Research and International Studies, Universiti
goal in each trial t (t = 1, . . . , 400) was to select (click
Sains Malaysia, 11800 Penang, Malaysia. Email: takemi@usm.my.
on) one of the two unmarked buttons that appeared on the
429

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Judgment and Decision Making, Vol. 4, No. 5, August 2009
The hot stove effect
430
of the assumed tendency to rely on small samples, and of
Table 1: Choice problems in Barron and Erev (2003) and
the hot stove effect. For example, all the leading models
Erev and Barron (2005). PH (PL) is % of H (L) choices
in a recent choice prediction competition that focused on
over 400 rounds.
repeated decisions from experience can be described as
Problem
H
PH
L
PL
alternative quanti?cations of these assumptions (see Erev
et al., 2009). However, some of the recent results appear
1
4, 0.8
63%
3, 1
37%
to question Erev and Barron’s (2003) conclusions with
(N =48)
regard to the relative magnitude of the two effects. Re-
2
view of Erev and Barron (2003) suggests that the clear-
4, 0.2
51%
3, 0.25
49%
(N =48)
est indications for underweighting of rare events come
3
from studies that examine decisions from experience with
32, 0.1
28%
3, 1
72%
(N =48)
complete feedback (e.g., Ert & Erev, 2007). This design
controls the hot stove effect with the provision of com-
plete feedback.
A different picture is, however, shown in studies that
computer screen. Each click resulted with an immediate
focus on decisions from experience with limited feed-
payoff (random draw from the payoff distribution asso-
back (e.g., Fujikawa, 2007; Fujikawa & Oda, 2007): the
ciated with the selected button). Thus, the prior infor-
feedback is limited to the obtained payoff, and the fore-
mation was minimalistic, and the participants had to base
gone payoff (the payoff from the unselected option) is
their decisions on experience. The participants deviated
not presented. These studies reveal strong underweight-
from maximisation. Table 1 shows the maximisation rate
ing of attractive rare events (when reliance on small sam-
(the overall proportion of H choices) in each problem: for
ples and the hot stove effect lead to the same predictions)
example, the overall proportion of H choices was 0.63 in
but no clear indication of underweighting of unattractive
Problem 1.
rare events (when the two tendencies lead to contradict-
In the data considered by Erev and Barron (2005), the
ing predictions). This verbal summary of the results is
tendency to rely on small samples appeared to be stronger
consistent with the predictions of the leading models in
than the hot stove effect. The clearest support for this
the choice prediction competition. For example, the best
conclusion came from Problem 1, which used the click-
baseline model (explorative sampler with recency in Erev
ing paradigm, where: (1) the participants were asked
et al. (2009)) predicts a H-rate of only 0.54 in Problem 1.
to select between unlabelled buttons on the computer
The main goal of the current paper is to clarify this
screen; (2) each selection/click led to a random draw from
picture: a picture that the hot stove effect is stronger than
the payoff distribution associated with the different but-
suggested by Barron and Erev (2003) and Erev and Bar-
tons; and (3) in choosing among possible options, the par-
ron (2005). In order to achieve this goal I implemented
ticipants had to rely on the immediate feedback obtained
Problem 1, 2 and 3. Note again that the hot stove ef-
in similar situations in the past.
fect implies a bias toward L (the low variability option)
Notice that in Problem 1 the worst outcome (0 from H)
in Problem 1 and 3.
is also the rare outcome (probability of 0.2). In Problem
1, reliance on small samples and the hot stove effect lead
to contradicting predictions. Reliance on small samples
2 Experiment
implies that the rare outcome (0 from H) will be under-
weighted: this prediction implies that H will be preferred.
The current experiment was conducted at the Kyoto Ex-
The hot stove effect predicts the participants’ learning
perimental Economics Laboratory (KEEL) in Japan with
that reduces their likelihood of repeating decisions, with
42 paid subjects — undergraduates from various facul-
which they have done poorly (i.e., getting burned on a
ties at Kyoto Sangyo University. On their arrival at the
hot stove in Twain’s example, and thus referring to earn-
KEEL, each participant was assigned a workstation that
ing the worst outcome from H). Thus, the hot stove effect
displayed an experimental screen, and distributed a writ-
implies that the worst outcome (0 from H) will be over-
ten instruction of the experiment. (The instruction and
weighted: this prediction implies that L will be preferred.
experimental screen are available in Appendix.) The in-
Barron and Erev (2003) and Erev and Barron (2005) re-
struction was read aloud and the participants were given
ported that the observed proportion of H choices (over
an opportunity to ask questions individually. The partic-
400 trials) was 0.63. Their results suggest that the ten-
ipants engaged in Problem 1, 2, and 3 in order. They
dency to rely on small samples is stronger than the hot
were instructed to operate a “computerised money ma-
stove effect.
chine” and to choose one of two unmarked buttons shown
Follow-up studies demonstrated the descriptive value
in Figure 1 which corresponded to H and L for 400 times

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Judgment and Decision Making, Vol. 4, No. 5, August 2009
The hot stove effect
431
screen on their completion of Problem 1. (The message is
presented in the instruction that is available in Appendix.)
Hence, they were aware when a change from Problem
Total points you have earned in this session
124
1 to Problem 2 was generated; that is, on their comple-
tion of Problem 1, they were advised that Problem 1 had
been completed and they moved on Problem 2. The same
procedure applied to when a change from Problem 2 to
Problem 3 was generated. At the conclusion of the ex-
periment, the participants were paid individually and pri-
vately at a conversion rate of one point to 0.3 Yen (about
0.25 US cent at the time of the experiment), and received
no initial (showing up) fee.
You win
4
3 Results and discussion
The overall maximisation rate (choiceH) is 0.48, 0.55 and
0.22 for Problem 1, 2 and 3 respectively. It follows that
Figure 1: Computerised money machine
H, for example, was chosen on average 192 out of 400
times in Problem 1. Figure 2 illustrates choiceH for each
problem. The individual choiceH is presented in Table 2.
in each of the three problems. They made a choice be-
tween the two unmarked buttons on a computer screen
0.6
to which each participant was assigned. In each trial t
(t = 1, 2, . . . , 400), the participants were asked to click
on one of the two buttons. Each click led to a random
0.5
draw from the outcome distribution associated with the
selected button. The participants were disclosed neither
0.4
prior information on possible outcomes and probabilities,
nor the exact length of the experiment.1 They could see
0.3
the drawn value (the obtained payoffs) after each trial on
their computer screens. That is, the information available
0.2
to the participants was limited to feedback concerning the
outcomes of their previous decisions. The money ma-
0.1
chine provided the participants with binary types of feed-
back immediately following each choice: (1) the payoff
for the choice that appeared on the screen for the dura-
50
100
150
200
250
300
350
400
tion of one second; and (2) an update of an accumulating
Trials
payoff counter, which was constantly displayed.
Problem 1
Problem 2
Problem 3
The protocol of the experiment was as follows. At ?rst,
the participants played Problem 1, 2 and 3; that is, they
were played 1200 trials in the experiment (400 trials for
Figure 2: choiceH in Problem 1, 2 and 3
each problem). As noted above, they were not informed
that they were to play exactly three choice problems, in
Here, I should like to raise a question as to what ex-
each of which the participants were presented with a 400-
tent ?nding of the deviation from maximisation in Bar-
fold repetition of a binary choice. Hence, the participants
ron and Erev (2003) and Erev and Barron (2005) — also
were not aware that they had 1200 trials to play in the
in my experiment — can be attributed to the hot stove
experiment. Instead, they were aware that they faced sev-
effect, which appears to be as important as the payoff
eral choice problems in the experiment. The participants
variability effect and the effect of reliance on small sam-
started with Problem 1 and made 400 selections in Prob-
ples (and underweighting of rare outcomes). The payoff
lem 1. Then, the participants were prompted to move to
variability effect is a change of preference between two
Problem 2 by the automatically-generated message on the
alternatives in experience-based binary decisions, associ-
ated with a change in the payoff variability of the alterna-
1The participants were informed at the time of recruitment that an
tives. In the current choice problems, the payoff variabil-
estimated duration of the whole experimental procedure was two hours.
ity effect is what makes the DMs move toward random

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Judgment and Decision Making, Vol. 4, No. 5, August 2009
The hot stove effect
432
Table 2: The individual overall choiceH in each problem,
Problem 1
Problem 2
Problem 3
grouped by prevalent patterns of responding. An abso-
lute difference of 5.5% or more from 50% is signi?cant
0.0175
0.5125
0.0025
(p < 0.05 after Bonferroni correction). In Problem 1, 16
0.2200
0.3600
0.0225
participants exhibited the stronger hot stove effect (i.e.,
0.0025
0.3475
0.0125
their choiceH is less than 0.5). In Problem 2, 17 partici-
pants behaved toward random choice (i.e., their choiceH
0.0025
0.4600
0.0100
is not signi?cantly deviated from 0.5). In Problem 3,
0.0350
0.4825
0.0150
more then half of the participants (26 of them) exhibited
0.0025
0.8775
0.0050
the stronger effect of underweighting of rare outcomes
and the stronger hot stove effect (i.e., their choiceH is
t
0.3400
0.7275
0.1575
less than 0.22).
0.3675
0.4925
0.0375
Problem 1
Problem 2
Problem 3
0.2275
0.5775
0.0725
0.0000
0.4700
0.0025
0.0000
0.6225
1.0000
0.3825
0.6175
0.0025
0.6250
0.7100
0.4900
0.2400
0.4550
0.3575
0.3350
0.6675
0.4850
0.2675
0.6175
0.1375
0.6875
0.5200
0.5725
0.1925
0.3450
0.3400
0.0950
0.5675
0.6000
0.0050
0.5325
0.0000
0.5525
0.3350
0.6425
0.7175
0.5575
0.4925
0.5600
0.6075
0.7125
choice between an alternative with higher expected value
and an alternative with lower expected value when the
0.5350
0.5100
0.5800
payoff variability is associated with the alternative with
0.7200
0.8775
0.4050
lower expected value in experience-based binary deci-
0.8250
0.4900
0.4800
sions. Speci?cally, when the payoff variability of an at-
tractive alternative (an alternative with higher expected
0.5175
0.5900
0.4825
value) increases, choice of the alternative decreases. On
the other hand, when the payoff variability of an unattrac-
0.6625
0.3900
0.0275
tive alternative (an alternative with lower expected value)
0.6575
0.5200
0.0200
increases, the DMs are sensitive to a bias toward random
0.9050
0.6600
0.0075
choice between both alternatives, rather than being sensi-
tive to expected values. Erev and Barron (2005) describe
0.7150
0.6550
0.2250
the payoff variability effect as an obvious class of failures
1.0000
0.4750
0.0175
to maximisation. As said above, when the higher payoff
0.5250
0.6725
0.0225
variability is associated with an attractive alternative, the
DMs would feel that it is less attractive. They then behave
0.7000
0.5075
0.1925
worse in terms of maximising expected value (by choos-
0.7475
0.5200
0.0675
ing an unattractive alternative often). When the higher
0.6025
0.4100
0.0050
payoff variability is associated with an unattractive alter-
native, they would be indifferent between an attractive
0.7725
0.5425
0.2025
and unattractive alternative so as to move toward random
0.9925
0.4075
0.0075
choice between both alternatives.
0.9300
0.6625
0.0300
Denrell and March (2001) document that the hot
stove effect implies a bias against a risky alternative in
0.8425
0.5250
0.0125
experience-based decisions, and the bias is a product of
0.6800
0.5800
0.0250
the tendency to reproduce actions that have been success-
0.9750
0.5525
0.1400
ful and avoid actions that led to loss. Thus, the hot stove
effect implies a bias toward L (the low variability option)
in Problem 1, 2 and 3. Here is the explanation that low
payoffs from H reduce the probability of additional H

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Judgment and Decision Making, Vol. 4, No. 5, August 2009
The hot stove effect
433
choices, and for that reason their effect of the estimated
variability is not associated with L in Problem 1 and 3,
value from H is large. In an extreme case, a sequence
as it only yields a sure payoff of three points in the two
of two “0” outcomes in Problem 3 can eliminate addi-
problems. When the payoff variability of an unattractive
tional H choices and keep the participants’ estimate that
alternative is maximal, the payoff variability effect im-
H yields only “0” outcomes.
plies a bias toward random choice: in Problem 2, both
In Problem 1, reliance on small samples (and thus the
alternatives yield worst outcomes (“0”) for most of the
effect of underweighting of rare outcomes) leads to the
rounds (i.e., 80% from H and 75% from L). Hence, the
prediction, implying more H choices. Central to this pre-
participants might have been considered to be indifferent
diction is the supposition that H provides better payoff (4
between H and L. This might have caused a bias toward
vs. 3) in most of trials (80%). The results of Barron and
random choice. However, I observed 55% H choices in
Erev (2003) and Erev and Barron (2005) suggest that the
Problem 2 in the current experiment. This phenomenon
hot stove effect is not very strong: they observed almost
seems to be caused by existence of the two effects —
60% H choices in Problem 1. On the contrary, I observed
the payoff variability effect and the attenuated hot stove
almost 50% H choices in Problem 1 in the current exper-
effect. The payoff structure in Problem 2 is more com-
iment. The current results can be summarised with the
plicated than that in Problem 1 and 3, as both H and
assertion that they re?ect a stronger hot stove effect that
L involve uncertain prospect in Problem 2. Hence, the
implies more L choices. It seems that the two effects (the
hot stove effect is attenuated in Problem 2, as there is
hot stove effect and the effect of underweighting of rare
more decay of the participants’ memory of past experi-
outcomes) cancel each other and choiceH is close to 50%
ence in Problem 2 than in Problem 1 and 3. Thus, both
in the current experiment. The hot stove effect appears to
two effects can account for 55% H choices in Problem 2
be as important as reliance on small samples (the effect
in the current experiment: (1) the payoff variability ef-
of underweighting of rare outcomes), though Barron and
fect, implying a bias toward random choice; and (2) the
Erev (2003) and Erev and Barron (2005) seem to have
attenuated hot stove effect, implying a bias toward less L
paid little attention to the hot stove effect in analysing
choices.
behavioural tendencies in Problem 1.
In Problem 3, reliance on small samples — that causes
underweighting of the attractive rare outcome (32 from
4 Concluding remarks
H) — leads to the same prediction as the hot stove effect:
it implies more L choices. Central to this prediction is the
This paper has revisited the roles of mechanisms of indi-
supposition that L provides better payoff (0 vs. 3) in most
vidual decision making in experience-based decisions to
of trials (90%). Results in Barron and Erev (2003) and
complement a work of Barron and Erev (2003) and Erev
Erev and Barron (2005) reveal strong reliance on small
and Barron (2005). They showed that the participants de-
samples (underweighting of the attractive rare outcome)
viated from maximisation. They argued that the partici-
when both reliance on small samples and the hot stove
pants’ choice mainly re?ected the payoff variability effect
effect lead to the same predictions, though the authors do
and the effect of underweighting of rare outcomes.
not further discuss the hot stove effect. They observed
In this paper, I replicated the choice problems in Bar-
almost 30% H choices in Problem 3. On the contrary, I
ron and Erev (2003) and Erev and Barron (2005) to re-
observed almost 20% H choices in Problem 3. The cur-
examine their results. Consistent with their results, the
rent results suggest that the participants’ less selection of
participants in the current experiment deviated from max-
H is the consequence of both the effect of underweight-
imisation. The current results suggested that choices
ing of rare outcomes and the hot stove effect, as the two
were consistent with the prediction of the hot stove effect
effects lead to the same prediction in Problem 3 (a bias
in addition to the payoff variability effect and the effect
toward L).
of underweighting of rare outcomes. Although the hot
I suggest that both the payoff variability effect and the
stove effect was not further discussed in Barron and Erev
hot stove effect can account for behavioural tendencies
(2003) and Erev and Barron (2005), I found that the effect
in Problem 2, though much attention to the latter is not
appears to be as important as the payoff variability effect
given by Barron and Erev (2003) and Erev and Barron
and the effect of underweighting of rare outcomes in ex-
(2005). They observed almost 50% H choices in Prob-
amining the behavioural tendencies in experience-based
lem 2. Their results suggest that choice behaviour moves
decisions. These conclusions are consistent with the fact
toward random choice in Problem 2, where the payoff
that most of the clearest demonstrations of underweight-
variability is associated with an alternative with lower ex-
ing of rare events were observed in environments that
pected value — an alternative L.2 Note that the payoff
3.2)2 + 0.2(0 ? 3.2)2 = 2.56, Variance of H in Problem 2, s2 , =
H2
0.2(4 ? 0.8)2 + 0.8(0 ? 0.8)2 = 2.56, and Variance of L in Problem
2We can measure the payoff variability for an alternative that has
2, s2 , = 0.25(3 ? 0.75)2 + 0.75(0 ? 0.75)2 = 1.6875. Variance
L2
two outcomes as follows: Variance of H in Problem 1, s2 , = 0.8(4 ?
of L in Problem 1 is zero.
H1

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Judgment and Decision Making, Vol. 4, No. 5, August 2009
The hot stove effect
434
control the hot stove effect by the addition of informa-
• Questionnaire form
tion concerning the forgone payoffs, with free sampling,
or with forced sampling.
• Receipt form
• Subject NO card
References
Receipt Please write in the form your name, ID number,
address, and the date today in advance. Keep the amount
Barron, G. & Erev, I. (2003). Small feedback-based deci-
blank.
sions and their limited correspondence to description-
Notice
based decisions. Journal of Behavioral Decision Mak-
• You may NOT create a disturbance.
ing, 16, 215–233.
Coutu, D. (2006). Ideas as art. Harvard Business Review,
• You may NOT leave the laboratory during the exper-
84, 82–89.
iment.
Denrell, J. & March, J. (2001). Adaptation as information
restriction: The hot stove effect. Organization Science,
• You may keep switching your portable phone off
2, 523–538.
during the experiment.
Erev, I. & Barron, G. (2005). On adaptation, maxi-
• You must leave all items distributed by personnel in
mization, and reinforcement learning among cognitive
the laboratory.
strategies. Psychological Review, 112, 912–931.
Erev, I., Ert, E., Roth, A., Haruvy, E., Herzog, S., Hau,
• You may NOT touch a keyboard.
R., Hertwig, R., Stewart, T., West, R. & Lebiere, C.
• Do NOT click on right.
(2009). A choice prediction competition, for choices
from experience and from description. Manuscript
• You may NOT attempt to tamper with a computer.
submitted for publication.
Failure to comply with administrator’s directions can re-
Ert, E. & Erev, I. (2007). Loss aversion in decisions un-
sult in points you earned being cancelled and no money
der risk and the value of a symmetric simpli?cation of
will be paid.
prospect theory. Technion, Working Paper.
If you need an administrator If at any time during the
Fox, C. R., & Hadar, L. (2006). “Decisions from experi-
experiment you believe you have a problem with your
ence” = sampling error + prospect theory: Reconsider-
computer or need an administrator for any reason, raise
ing Hertwig, Barron, Weber & Erev (2004). Judgment
your hand.
and Decision Making, 1, 159–161.
Payment At the conclusion of the experiment, points will
Fujikawa, T. (2007). Perfect bayesian vs. imperfect
be converted to monetary payoff according to the ex-
bayesian in small decision making problems. Behav-
change rate: 100points =30yen. The amount below 10
iormetrika, 34, 27–44.
yen is rounded up.
Fujikawa, T. & Oda, S. H. (2007). Judgement in small
Procedure
decision-making problems. In S. H. Oda (Eds.), De-
Registration Check that Figure 1 is displayed on your
velopments on Experimental Economics, pp. 149–154.
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Germany: Springer Verlag.
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appeared on the screen with your subject number then
Appendix
press “Correct”. Assuming that your subject number is
19, press “Correct” in Figure 2.
Instruction (translation from Japanese)
Introduction
Thank you very much for joining our economics ex-
periment. In this experiment you are asked to play easy
games. Your goal is to complete the experiment with as
many points as possible. The more points you earn, the
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Distributions Please con?rm whether you have received
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• Instruction (This lea?et)
Figure 1

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Judgment and Decision Making, Vol. 4, No. 5, August 2009
The hot stove effect
435
Total points you have earned in this session
19
124
Figure 2
You win
4
Figure 4
Total points you have earned in this session
Figure 5
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Figure 6
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You win
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different session has the different structure of the experi-
ment. Your score is not affected by other’s behaviour. An
Figure 3
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on the right side of “Total points you have earned in this
session”. After completing each session, Figure 5 ap-
pears. Then Figure 6 appears after pressing “OK” in the
Figure 5.
How to operate? The experiment consists of several ses-
sions. Each session consists of several rounds. You are
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round as seen in Figure 3. The points corresponding to
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(see Figure 4 as an example) and you can get it at that
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