On the Reliability of Reciprocal Fairness *
- An Experimental Study -
Werner Güth
Nadège Marchand
Jean-Louis Rullière
Humbodt-University of Berlin,
Groupe d’Analyse et de
Groupe d’Analyse et de
Department of Economics,
Théorie Economique (GATE), Théorie Economique (GATE),
Institute for Economic Theory,
UPRES A 5048 du CNRS,
UPRES A 5048 du CNRS,
Spandauer Str. 1, D - 10178
93, Chemin des Mouilles,
93, Chemin des Mouilles,
Berlin, Germany
69130 Ecully, France
69130 Ecully, France
*
Support from the Deutsche Forschungsgemeinschaft (SFB 373, Quantifikation und Simulation
ökonomischer Prozesse) is gratefully acknowledged.
2
Abstract
Fairness is a robust phenomenon in ultimatum bargaining
although it has to compete with other concerns. An effective
mean to eliminate fairness has been role competition (Prasnikar
and Roth, 1992). It is explored whether after an initial phase of
responder competition or random respondership fairness will
regain its influence. In both treatments participants first
experience
random
respondership,
respectively
responder
competition before playing a usual ultimatum game. A control
treatment employs only the second phase.
JEL classification : C72, C78, C92
3
1. Introduction
There is convincing evidence that people can effectively cooperate even in situations
where cooperation is endangered by opportunistic exploitation. In employment
relationships (especially, but not only) in the public sector, one often does not rely on
elaborate incentive schemes, but on trust that the employee repays in reasonable effort.
Whenever trust in others’ willingness to cooperate is rewarded, we speak of reciprocal
fairness.
Experimentally
reciprocal
fairness
in
employment
relationships
is
convincingly demonstrated by Fehr, Gächter and Kirchsteiger (1996) as well as by Güth,
Klose, Königstein and Schwalbach (1996). More abstractly, also the typical behavior in
ultimatum bargaining can be justified this way (see Güth, 1995, Roth 1995, and
Camerer and Thaler, 1995, for surveys).
Here we will focus on the ultimatum game as the paradigm for investigating the
reliability of reciprocal fairness. One effective way of endangering reciprocal fairness in
this context is to introduce role competition for becoming the decisive responder: five
potential responders compete for this position by individually choosing an acceptance
threshold and the actual responder is the one whose acceptance threshold is minimal.
Prasnikar and Roth (1992) have convincingly demonstrated how role competition can
lead to results closely resembling the game theoretic solution. Thus responder
competition effectively endangers reciprocal fairness in the ultimatum game.
A less extreme form of role assignment is to let the decisive responder be randomly
chosen, (random respondership). After experiencing responder competition or random
respondership all participants finally play the same (ultimatum) game. Will those who
have experienced very unfair payoff distributions play less fair in this final game or is
reciprocal fairness strong enough to recover immediately? Of course, already the fact
that there are five potential responders may weaken the influence of fairness due to the
more problematic equity considerations (only one of 5 potential responders can win). In
a control experiment we have checked the behavior of participants with no previous
experience of responder competition or random respondership. These participants
played just the final ultimatum game where every responder is decisive.
4
To rely as far as possible on the same instructions we have used the notion of a decisive
responder who is actually responding to the offer made by the proposer. With
responder competition the decisive responder is a potential responder whose acceptance
threshold is minimal. With random respondership the decisive responder is a randomly
selected potential responder. The instructions for the initial phase only differ in a small
paragraph describing the respective rule determining the decisive responder.
During the second phase all 5 responders were decisive in the sense that their
acceptance threshold decided whether or not they accept the amount offered by the
proposer. To avoid that proposers earn more than once what they demand for
themselves their payoff was determined by a randomly selected acceptance threshold.
This is the only change from the first to the second phase. Whereas the first phase
extends over five successive rounds of ultimatum bargaining, the second phase consists
of one round only.
In section 2 we describe our experimental procedure in more detail, specify some
hypotheses in section 3, and then (section 4) illustrate our experimental observations. In
section 5 we test the main hypothesis of robust reciprocal fairness. In section 6 we
summarize our main results.
2. Experimental design
Using the same terminology as in the instructions let X be the proposer in ultimatum
bargaining and Y1, ... Y5 the five potential responders. In both phases of the experiment
(see Appendix A for the instructions with responder competition and the alternative
paragraph for random respondership) participants are interacting in groups of 6
participants, one X and five potential responders Y1, ... Y5. After the first phase two such
groups (with random respondership, respectively responder competition) exchanged
their proposer X to weaken the influence of repeated interaction.
The second phase is identical for all treatments, (responder competition, random
respondership, no previous experiences). Participants always play an ultimatum game in
the strategy method with monotonic responder strategies (see Appendix B for the
instructions). This means that the responder has to choose his acceptance threshold
5
before knowing the offer y of the proposer with 0 ≤ y ≤ c and c=50 ECU (Experimental
Currency Unit). By his acceptance threshold y i responder Yi accepts all offers y ≥ y i
whereas offers y < y i are rejected. In previous studies (see the survey by Güth and Tietz,
1990) the strategy method has been shown to strengthen fairness considerations.
Proposer X can make only one offer y. Thus the 6 participants actually play one game
and not 5 isolated games. This, however, does not change the game theoretic solution
for players who are only interested in their monetary earnings: any (monotonic)
responder strategy y i with y i > ε is (weakly) dominated. Here, ε is smallest possible
monetary unit (since we only allowed for integer offers y in the experiment, y = ε
corresponds to offering one ECU). Anticipating that all offers y ≥ ε will be accepted
renders y * = ε or y * = 0 as optimal like in usual ultimatum games.
Our data file is based on 25 groups, namely 12 groups with responder competition, 10
groups with random respondership, and 3 groups with no previous experiences. The
altogether 150 participants were invited to register for the experiment. On arrival
participants received their code which also determined their role as an X or Yiparticipant in the group. All X-participants were in one room, two other rooms
accommodated the Yi-participants.
According to the experimental protocol (Appendix A) first the 1. instructions (Appendix
B) were read. After answering questions privately participants received all the same 1.
control questionnaire (Appendix B) before playing the 5 successive rounds of the first
decision phase with random respondership, respectively with responder competition.
During the whole experiment the only information feedback was what a participant has
earned in the previous round. On the decision form we also asked for expectations
concerning the behavior of the other bargaining side (see Appendix D, this decision
form was also used in the 2nd phase of the experiment).
After the first decision phase (which, of course, was missing in case of no previous
experiences) we distributed the instructions (Appendix C) for the 2nd phase which were
the same for all groups and all three treatments. Again we answered questions privately
6
before distributing the 2. control questionnaire (Appendix E). A proposer was now
matched with another responder group of the same treatment. Participants then played
the 6th round in which all five participants are actively playing against X. Here X’s
payoff is determined by confronting his or her offer y with a randomly selected
acceptance threshold y i with i = 1, 2, ..., 5. The experiment concluded by answering the
Post-Experimental Questionnaire (Appendix F) and then paying the monetary wins
privately.
3. Hypotheses
Prasnikar and Roth (1992) show that with role competition a game theoretic type of
behavior has to be expected. To the best of our knowledge random respondership has
not yet been tested experimentally. Like responder competition random respondership
excludes equal payoffs since at most one of the 5 potential responders Y1 to Y5 can win.
This also should weaken the influence of fairness, but less than competition for
becoming the unique responder. In view of the typical results of ultimatum bargaining
(one typically observes
c
c
≤ y ≤ ) we therefore expect
3
2
Hypothesis G(amesmanship):
At the end of the 1. decision phase the average offers y and the mean
acceptance thresholds y i will be smaller than 50/3 and smaller in case of
responder competition than in case of random respondership. All averages
should decrease from round 1 to round 5 of the first decision phase.
Even when the differences between random respondership and responder competition
are less dramatic, they should be clearly visible. After all potential responders face a
fierce form of the Bertrand-price competition in case of responder competition, whereas
they do not directly interact strategically in case of random respondership. We do not
expect that behavior is similar for those who previously experienced random
respondership, or responder competition, or those with no previous experiences :
Hypothesis R(esistant effects of responder competition) :
7
In the second decision phase the average offers y as well as the mean
acceptance thresholds y i will be lower after responder competition than
after random respondership which, in turn, will be lower that in case of no
previous experiences.
From the answers of the two control questionnaires (Appendices B and C) we know that
some participants at least initially did not understand the situation completely. In our
view, a basic misunderstanding can lead to decisions which are rather inadequate. We
therefore expect a wider variance of individual decisions from those, who initially did
not perceive the situation properly, than from those who answered all control questions
correctly :
Hypothesis V(ariance increase by incorrect answers to control questions):
At least in the first rounds of the first decision phase and in the second
decision phase the variance of individual offers y and of the individual
acceptance thresholds y i will be larger for participants who have not
answered the control questions correctly.
4. Experimental results
The 10 plays with random respondership (RR), the 12 plays with responder competition
(RC), and the 3 plays of no previous experiences (NPE) for all 25 groups are listed in
Table I (the individual data can be found in Appendix G). It gives the offers y and
whether they are accepted (δ = 1) or not (δ = 0) for all successive rounds where for
round 6 we give all acceptance thresholds y i with i = 1, ..., 5. A graphical illustration of
the 22 offer sequences can be found in Figures 4.1a and 4.1b. How average offers
develop is illustrated by Figure 4.3.
The average offer with responder competition is clearly below that one with random
respondership. There is a general erosion of fairness (mean offers usually decline during
the 1st decision phase). The discrepancy between RR and RC remains to a small extent
during the 2nd phase (round 6). There is, however, a very clear remaining effect in the
frequencies of 0-acceptance thresholds y i in round 6: Whereas in case of earlier random
8
respondership only 4 of 50 acceptance thresholds of the 2nd phase were 0, the
corresponding number for responder competition is 34 of 60 (see Table I). Thus former
experiences are not quickly forgotten. Figures 4.1a and 4.1b illustrate that for both
treatments there is a considerable variance in offer dynamics (see also the standard
deviations in Table I).
Rounds
decisions
y
35
21
20
22
20
RR
37
27
20
25
25
Σ/10
25,2
Stand. Dev 34,8
25
25
20
25
26
21
RC
20
20
20
20
10
25
Σ/12
21,4
Stand. Dev 17,7
1
2
δ
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
y
25
22
30
18
27
30
30
20
1
10
21,3
82,6
20
10
17
15
23
20
18
15
25
20
10
20
17,8
19,7
3
δ
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
NPE
Σ/3
Stand. Dev
y
25
15
20
15
28
27
25
15
20
25
21,5
24,1
15
5
15
10
21
15
20
12
22
15
10
15
14,6
22,2
4
δ
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
y
25
10
15
15
26
21
18
10
10
10
16
35,6
10
8
10
8
13
14
15
10
20
13
10
10
11,8
10,9
5
δ
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
y
25
5
15
10
22
20
22
20
10
25
17
44
10
0
5
7
8
11
12
12
18
15
10
10
9,83
19,6
6
δ
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
y
20
6
26
10
30
25
15
20
20
25
19,7
50,6
25
6
20
20
14
20
27
y1
1
0
25
20
1
20
1
20
1
10
y2
20
0
5
10
0
1
1
17
15
15
y3
12
20
5
1
15
0
1
7
10
10
y4
5
1
10
5
1
23
5
10
1
10
y5
10
25
1
1
14
5
1
22
1
1
2
5
0
8
6
5
0
23
5
0
0
0
1
0
0
0
0
0
0
0
0
15
20
0
0
0
0
0
0
0
5
0
1
0
0
15
25
15
10
20
18,1
36,4
14
18
25
19
20,7
5
0
10
0
20
0
0
5
0
22
1
0
1
0
9
0
1
15
10
10
0
0
4
0
10
15
20
20
15
20
13
17
10
24
20
13
24
18
24
10
Table I : The plays with random respondership (RR), responder competition (RC) and
no previous experience (NPE).
∅y j
9,6
9,2
9,2
7,4
6,2
9,8
1,8
15,2
5,6
9,2
8
62,4
8
6
1
1,6
1,4
1,2
0
1,2
0,2
7
2
14,2
4
37
17
17,4
18,2
17,5
21,2
9
Offe rs per group in RR tre atme nt
40
35
30
G10
G9
G8
offers
25
20
G7
G6
15
G5
10
group numers
G4
G3
5
G2
0
G1
1
2
3
4
5
6
Rounds
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
Figure 4.1a: The offer sequences with random respondership.
Offers per group in RC treatment
40
35
30
G12
G11
G10
offers
25
G9
20
G8
G7
15
G6
G5
10
G4
Group numers
G3
5
G2
0
G1
1
2
3
4
5
6
Rounds
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
Figure 4.1b: The offer sequences with responder competition.
G11
G12
10
The dynamics of mean acceptance thresholds with and without responder competition
are graphically visualized in Figure 4.2. After nearly no difference in round 1 mean
acceptance thresholds for random respondership are much larger than those for
responder competition. This significant discrepancy remains in round 6 when for all
treatments the same game is played. Figure 4.2 reveals an unusual willingness to accept
unfair proposals: Offers y below 15 are acceptable although they assign less than 30 %
of the available amount to the responder. Willingness to refuse unfair offers does not
immediately recover in round 6.
The surprising willingness to accept unfairness for RC and RR could be a group size
effect and a consequence that fairness in the sense of equal treatment for all 6 group
members is impossible. Important is that the willingness to accept unfairness remains
when moving from the 1st to the 2nd phase. A clear indicator are the 38 (of 110) 0acceptance thresholds in round 6 (see Table I). Thus at least as far as responders are
concerned fairness considerations are not very reliable: After experiencing unfair
behavior they will not immediately regain their former importance.
Mean acceptance thresholds
Maen accpetance threshold
20
16
12
8
4
0
1
2
3
4
5
6
Rounds
random respondership
Figure 4.2:
responder competition
NPE
The dynamics of mean acceptance thresholds with and without responder
competition ( ∗ – the mean NPE-offer)
11
Mean offers
25
Mean offers
20
15
10
5
0
1
2
3
random respondership
Figure 4.3:
Rounds
4
responder compet it ion
5
6
NPE
The dynamics of mean offers with and without responder competition
( ∗ – the mean NPE-threshold)
5. Evaluation of hypotheses
To examine Hypothesis G claiming gamesmenship in the sense that mean offers y and
acceptance thresholds y are smaller than 1/3 of the pie let us first look at the mean
i
offers (the ∅ y-line of Table II). In case of random respondership (RR) fairness erodes
more slowly than for responder competition. With responder competition (RC) only in
rounds 1 and 2 the average offer exceeds 50/3. The mean acceptance thresholds strongly
confirm hypothesis G although erosion is much slower in case of random respondership.
Altogether, especially for responder competition, hypothesis G is largely consistent with
the data.
Table II: The average results
12
In the 1rst round of the experiment there is no significant difference ( p = .681 ) between
the two treatments, RC and RR (RC1 and RR1). Repeating the game has, however,
significant effects on offers and acceptance thresholds. In the 5th round both, offers and
acceptance thresholds (measured by responder group means or medians), are
significantly1 higher for RR than for RC (RC5 and RR5). For RC erosion (RC1 and
RC5) is highly significant ( p < .01 ) for the sign test (ST) and the Wilcoxon-test (WT)
of the offers which, on average, drop from 21.4 to 9.8. The corresponding effect (RR1
and RR5) for RR is significant in the sense of p < .1 . Similar results hold for the
acceptance thresholds except for their medians in case of RR and WT where p = .63 .
Thus for RR the decline of acceptance thresholds in the course of the 1st phase appears
dubious.
Let us now investigate the influence of past experience on behavior during the 2nd stage
of the experiment (round 6). A benchmark are the results with no past experiences
(NPE) of 18 participants (3 groups of 6 participants) who had to decide only in the 2nd
phase (round 6). Past experiences have a significant influence on acceptance thresholds:
All p-levels are significant according to three statistical tests (KS, MW, WaldWolfowitz/WW) except when comparing responder competition (RC6) with NPE (here
only the KS and MW-test indicate significant effects). Regarding offers there are only 3
observations for the NEP-treatment. Generally participants, who have experienced
unfair results before, chose lower acceptance thresholds.
The reliability of fairness can be tested by comparing behavior in the 5th and the 6th
round in case of random respondership, respectively responder competition. The
acceptance thresholds of the 5th and 6th round of responder competition (RC5 and RC6)
do not differ significantly neither for means where p = .388 (ST) and .37 (WT) nor for
medians with p = .125 (ST and WT). There is however, a significant increase in the
offers between round 5 and 6 with p = .002 (WT and ST), whereas for RR the offers
are rather stable (no significant differences between RR5 and RR6, p = .453 (ST) and
1
Regarding offers the p -level are .021 and .011 for the Mann-Whitney (MW) U , respectively the
Kolmogorov-Smirnov-test (KS); regarding mean or median acceptance thresholds one always has
p ≤ .001 .
13
.234 (WT)). Regarding acceptance thresholds only means suggest unambiguously a
significant increase from round 5 to round 6 in case of RR ( p = .09 (ST) and .002
(WT), for medians one obtains p = .094 (WT) and .453 (ST)). Thus for both treatments
(RC and RR) the acceptance thresholds are rather stable, but on (significantly) different
levels. There is, however, a significant increase in the offers of the RC treatment, but
not in those of the RR-treatment.
Conclusion :
• Fairness is partly restored after the initial phase since proposers do
not (dare to) offer as little as before.
• Responders’ aspirations hardly recover, but rather remain on the last
low level of the initial phase.
In essence, this means that proposers could have offered less in the second decision
phase. The offers y maximizing the proposer’s expected profit when being randomly
matched with one of the responders are y = 10 or 15 for RR and y = 5 or 10 for RC.
Proposers either entertained wrong expectations or were simply more generous in the
2nd decision phase (during the 1st decision phase proposers earned on average much
more than a potential responder). Actually proposers on average expected only a minor
increase of the lowest acceptable offer from round 5 to round 6 (from 10 to 11.5 for RR
and from 6 to 13 for RC, see the ∅ y$ -line of Table II). It seems that RC-proposers
i
were more influenced by fear of rejection than RR-proposers when deciding in round 6.
Remember that proposers switched groups after the 1st phase. Thus in phase 2 one
cannot compensate those who have suffered from own greed before. Generosity on the
other hand is strengthened since in the 2nd phase a generous offer increases largely what
the group of players in total receives. If in round 6 proposer X increases the offer y by ∆
y, his own cost are ∆ y, but he gives ∆ y more to each responder.
In round 6 the mean offers and acceptance thresholds are lower for RC than for RR as
predicted by Hypothesis R. For RR one has ∅ y = 19,7 in round 6 and for RC only 18,1.
This difference is, however, insignificant unlike the difference for mean acceptance
thresholds where in round 6 one has ∅ y = 8 for RR and ∅ y = 4 for RC (p < .001).
i
i
14
Thus hypothesis R for acceptance thresholds y i is confirmed although the means are
pretty close.
Hypothesis V, predicting a wider variance in decision behavior of those who poorly
understood the instructions, can be tested by distinguishing the altogether
(50 − 40) + (60 − 44) = 26
potential responders who have not understood the 1st
instructions and the (50 − 38) + (60 − 52) = 20 responders who partly misunderstood the
2nd instructions. For proposers the corresponding numbers are (10 − 8) + (12 − 12) = 2
and (10 − 7) + (12 − 10) = 5 . In Table III we list the numbers of wrong answers to both
questionnaires (the 1st questionnaire applies to rounds 1 to 5, the 2nd to round 6)
separately for role X and Yi and for treatments RR, RC and NPE. In total the number of
incorrect answers did not decrease from the 1st to the 2nd decision phase (RR and RC).
The number of participants, who answered both questionnaires correctly, is 73 of 110.
There is a small group of 11 participants who consistently had difficulties to understand
the rules and a larger group of 26 participants who fail only for one situation (they may,
of course, have been only sloppy).
Table IV distinguishes between the two treatments RR and RC. Each matrix component
lists the standard deviation σ y of the offers y (left entry) and the standard deviation σ y
i
of acceptance thresholds y i (right entry). For potential responders Yi Hypothesis V is
invariantly confirmed since always the variance σ y of those, who answered correctly
i
(answer = 1), is smaller than the one of those who did not (answer = 0). For proposers
we partly cannot check Hypothesis V (the 1st decision phase of RC all proposers
answered correctly, see Table IV) and, if possible, we do not confirm Hypothesis V. Of
course, there are 5 times as many potential responders than there are proposers.
Nevertheless according to our data basis one should restrict Hypothesis V to potential
responders.
15
Round
1 to 5
6
role
X
Yi
X
Yi
treat-
RR
2 of 10
10 of 50
3 of 10
12 of 50
ment
RC
0 of 12
16 of 60
2 of 12
8 of 60
NPE
_
_
0 of 3
0 of 15
Table III: The numbers of wrong answers in the 1st and 2nd decision phase and
separated by roles (X versus Yi) and treatment
Rounds
1
2
3
4
5
6
σ y σ y i σ y σ y i σ y σ y i σy σ yi σ y σ y i σ y σ y i
Roles
RR answer
Treatments
RC answer
0
1
7,0 13 1,5 9,8 5,0 8,7 4,5 11 10 11 3
7,1 8,7 4,9 8,4 5,3 8,5 4,9 9 4,7 9,4 8
7,8
7
0
* 8,3 * 10,3 * 6,8 * 7,6 * 7,8 3
2,5 8,5 3,9 6,6 5,1 5,3 5,2 5,6 3,8 2,5 5
2,1
5
1
NPE answer
0
* *
20,7 0,3
1
Table IV: The standard deviations σ y and σ y of offers y and acceptance thresholds
i
y i separately for the groups of those who answered the 1st (rounds 1 - 5)
and 2nd (round 6) questionnaire (in)correctly
6. Conclusions
Fairness considerations matter (as shown by numerous studies of ultimatum bargaining),
but have to compete and actually may be dominated by other motivational forces as
originally demonstrated by Prasnikar and Roth (1992). Thus the question is not so much
whether people are fair or reciprocate (respond in kind), but rather when they do so.
Here we have concentrated on two aspects: Will people immediately reciprocate or be
fair as usual when they just have experienced no or nearly no reciprocity or fairness?
Will in 6-person ultimatum bargaining fairness be as strong as in usual ultimatum
bargaining?
One rather general result is that responders quickly learned to accept unfair offers and
did not immediately increase their acceptance thresholds after the initial phase. The
16
main treatment effect was observed for average offers ∅ y which decrease from 25.2 in
round 1 to 17 in round 5 and jump up again to 19.7 in case of RR whereas for RC it
starts out with 21.4 in round 1, goes down to 9.8 in round 5 and recovers to 18.1 in
round 6.
The surprising asymmetry in behavior (reliable fairness of proposers and learned stable
willingness of responders to accept unfair offers) can be partly (for RC) explained by
false expectations. Other possible explanations are the efficiency increase by generous
offers in round 6 or simply proposer generosity to compensate (a, however, different
group of) responders for rather low earlier earnings.
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Zurich.
Prasnikar, V. and A. E. Roth (1992). « Considerations of fairness and strategy:
Experimental data from sequential games », Quarterly Journal of Economics,
August, 865 - 888.
Roth, A. E. (1995). « Bargaining Experiments », in The Handbook of Experimental
Economics, pp. (J. H. Kagel, and A. E. Roth, Eds.), Princeton : Princeton Univ.
Press., Princeton, New Jersey.
17
Appendix A
Protocol :
1. Random assignment of participants to three rooms.
2. Participants playing the proposer role, respectively the one of a potential responder
(of the same treatment) meet in one room. All potential responders in the same room
thus receive the same instruction.
3. Privately answering questions.
4. Distributing, answering and collecting control questionnaires with attached code
cards.
5. Distribution of 1. decision forms and of record sheets (for first 5 rounds only),
Collecting decision forms,
Information feedback about earnings,
similarly for round 2, 3, 4, 5.
6. Distributing 2. instructions.
7. Privately answering questions.
8. Distributing, answering and collecting control questionnaires.
9. Distributing 6. decision forms and record sheets (of round 6),
Collecting decision forms,
Information feedback about earnings.
10.Post-experimental questionnaire.
11.Privately paying earnings.
18
Appendix B
1. Instructions (with responder competition)
You will be interacting in groups of 6 participants. One participant, we name him or her
X, assumes a special role since (s)he- and only (s)he - can propose how to divide an
amount of 50 French Franc between him or her and another person. (S)he does this
simply by deciding about his or her offer y to the other person. For the integer number y
the condition 0 ≤ y ≤ 50 must hold.
How do we determine whether X's offer y to some of the remaining five participants is
accepted or not and what the various participants will earn? Each of the remaining five
participants, we refer to them as Y1 , Y2 , Y3 , Y4 , and Y5 , must choose an acceptance
threshold y i with 0 ≤ y i ≤ 50 meaning that (s)he is only willing to accept offers y
satisfying y ≥ y i, i.e. if Yi would be decisive and if y < y i participant Yi would reject
X's offer y; if participant Yi would be decisive and if y ≥ y i then Yi would accept X's
offer y.
..........
How do we determine who of the participants Yi is decisive ? It is simply the participant
Yi whose acceptance threshold yi is smallest, i. e. the decisive participant Yi must
satisfy y i ≤ y j for all j=1, 2, 3, 4, 5 (if more than one Yi has the minimal y i, all these
participants have the same chance of assuming that role).
...........
What are the monetary consequences of this ? This is very straightforward. If y ≥ y i, the
decisive participant Yi receives y and participant X the amount 50-y which (s)he
wanted to keep. All the other participants receive nothing. If y < y i, all participants
receive nothing.
The same group of 6 participants will be interacting in this way not only once, but
successively. More specifically, there will be 5 rounds of interaction according to the
19
rules described above. After each round you will be informed by us about your own
earning which you will receive in cash after the end of the experiment.
Throughout the 5 rounds you will keep your position, i.e. the person, selected to be X,
remains to be X in all the 5 rounds and the person, selected to be Yi for i=1, 2, 3, 4 and
5, remains Yi in all 5 rounds.
Please, raise your hand if you did not understand these instructions. We will try to
answer your questions privately. Any public announcements or questions are strictly
forbidden. We thank you for your co-operation.
Instructions (for random respondership)
Only change is that the paragraph between the dotted lines is substitued by:
How do we determine who of the participants Yi is decisive ?
It is simply a randomly selected participant Yi where all the 5 participants Y1 , Y2 , Y3 ,
Y4 , and Y5 have an equal chance of becoming decisive.
20
Questionnaire 1:
Code
(Please, fill in you code!)
Before you actually decide, we kindly ask you to answer the following questions. Please,
answer them completely even if you are not completely sure how to answer.
Imagine that the decisive Yi-participant has chosen an acceptance threshold of 27. What
will participant X, the decisive Yi-participant and the other Yi-participants earn in case
of the following offers y by X ?
In case of the offer y = 21
X will earn _________________ .
The decisive Yi-participant will earn _________________.
The other Yi-participants will earn __________________ .
In case of the offer y = 37
X will earn _________________ .
The decisive Yi-participant will earn _________________.
The other Yi-participants will earn __________________ .
21
Appendix C
Instructions (second part)
You will be interacting again in groups of 6 participants. If you before assumed the role
of X, you will remain in this position; the same applies to participants assuming the
roles of participants Y1 , Y2 , Y3 , Y4 , and Y5 , respectively. Notice, however, that X is this
time confronted with a different group of five Y1 , Y2 , Y3 , Y4 , and Y5 - participants.
As before participants X must choose an offer y with 0 ≤ y ≤ 50 whereas the Yi participants with i = 1, 2, 3, 4, and 5 choose an acceptance threshold yi with
0 ≤ yi ≤ 50 .
How do the monetary earnings depend on this ? If y ≥ yi , then the Yi - participant
receives the offered amount y, if y < yi , then Yi earns nothing (i = 1, 2, 3, 4, and 5).
The monetary win of X is determined by selecting one of the 5 acceptance thresholds
with equal chances for all i = 1, 2, 3, 4, and 5. If for the randomly selected acceptance
threshold yi one has y ≥ yi , then X receives c-y, otherwise his monetary win is 0.
22
Appendix D
Code
(please, insert your code number!)
Decision Form (Y)
You are deciding in the role of Yj !
_____________________________________________________________________
Before deciding, please, answer the following question :
Which offer y by X do you expect ?
I expect X to offer y = _________
(only values y = 0, 1, ...., 50 are possible).
______________________________________________________________________
Now your decision :
I choose y j = __________
(only values y j = 0, 1, ..., 50 are possible).
______________________________________________________________________
Code
(please, insert your code number!)
Decision Form (X)
You are deciding in the role of X !
______________________________________________________________________
Before deciding, please, answer the following question :
What is, in your view, the lowest accepted offer y ?
I expect y = _______ as the lowest acceptable offer y
(only values y = 0, 1, ...., 50 are possible)
______________________________________________________________________
Now your decision :
I offer y = _________
(only values y = 0, 1, ..., 50 are possible).
______________________________________________________________________
23
Appendix E
Questionnaire 2.:
Code
(Please, fill in you code!)
Imagine the various acceptance thresholds are y 1 = 27, y 2 = 13, y 3 = 6, y 4 = 41 and
y 5 = 33. What would the various participants earn in case of the following offers y by
X?
In case of an offer y = 19 by X:
Participant
X
Y1
Y2
Y3
Y4
Y5
would earn
Participant
X
Y1
Y2
Y3
Y4
Y5
would earn
In case of an offer y = 31 by X:
24
Appendix F
Post-experimental questionnaire:
Code
(Please, fill in you code!)
(1) If you would be asked to give advice to all 6 participants which decisions would
you recommend for the first 5 rounds (i.e. you would play this role in the 5
successive rounds) and the 6. round respectively ?
first five rounds
6. round
X should offer y =
Y1 should choose y 1 =
Y2 should choose y 2 =
Y3 should choose y 3 =
Y4 should choose y 4 =
Y5 should choose y 5 =
(2) If you could buy the roles of the various parties in the experiment, how much
would you be willing to pay for them. Please, answer the questions separately for the
first five rounds (i. e. you would pay this role in the five successive rounds) and 6.
round, respectively.
first five rounds
6. round
For X I would be willing to pay at most :
For Y1 I would be willing to pay at most :
For Y2 I would be willing to pay at most :
For Y3 I would be willing to pay at most :
For Y4 I would be willing to pay at most :
For Y5 I would be willing to pay at most :
(3) Please, indicate on the following bipolar scales how you judge the experiment.
-4
-3
-2
-1
0
1
2
3
4
boring
interesting
relaxing
stressful
easy
difficult
cooperative
uncooperative
25
Appendix G
Rounds
decisions
RR
Σ/10
Stand. Dev
RC
Σ/12
Stand. Dev
^y i
1
y
1
20
5
15
15
20
24
20
5
2
13
66,8
0
5
20
20
18
20
15
20
15
10
10
15
14
39,3
35
21
20
22
20
37
27
20
25
25
25,2
34,8
25
25
20
25
26
21
20
20
20
20
10
25
21,4
17,7
δ
^yi
2
y
1
1
1
1
0
1
1
1
1
1
1
21
7
15
20
20
27
10
8
10
14
57,7
0
1
17
15
17
19
14
15
20
10
5
9
12
42,6
25
22
30
18
27
30
30
20
1
10
21,3
82,6
20
10
17
15
23
20
18
15
25
20
10
20
17,8
19,7
1
1
1
1
1
1
1
1
1
1
1
1
δ
^yi
3
y
1
1
1
1
1
1
1
1
0
0
1
15
6
15
21
20
25
10
9
12
13
48,2
0
0
15
10
17
14
15
12
18
10
3
7
10
36,7
25
15
20
15
28
27
25
15
20
25
21,5
24,1
15
5
15
10
21
15
20
12
22
15
10
15
14,6
22,2
1
1
1
1
1
1
1
1
1
1
1
1
4
y
δ
^y i
1
1
1
1
1
1
1
1
1
1
1
25
10 10
8
15
15 15
20 26
20 21
17 18
5
10
9
10
10 10
11,5 16
36,3 35,6
0
10
0
8
10 10
8
8
10 13
14 14
12 15
10 10
21 20
10 13
1
10
2
10
8 11,8
37,5 10,9
1
1
1
1
1
1
1
1
1
1
1
1
5
y
δ
^yi
1
1
1
1
1
1
1
1
1
0
1
25
5
5
8
15
10 10
20 22
16 20
20 22
6
20
7
10
10 25
10 17
37 44
0
10
0
0
5
5
7
7
7
8
11 11
10 12
12 12
15 18
10 15
0
10
0
10
6 9,83
26,6 19,6
1
1
1
1
1
1
1
1
1
1
1
1
NPE
Σ/3
Stand. Dev
Table G.1:
δ
^yi
6
y
1
0
0
1
1
1
1
1
1
1
1
10
10
10
18
20
15
20
5
6
11,5
38,9
25
0
10
8
8
20
20
15
15
10
9
16
13
42,7
13
13
15
14
0,89
20
6
26
10
30
25
15
20
20
25
19,7
50,6
25
6
20
20
14
20
27
15
25
15
10
20
18,1
36,4
14
18
25
19
20,7
1
1
1
1
1
1
1
1
1
1
1
1
Proposers expectations ( y$ i ), decisions (y) and responders reactions ( δ )
for the 6 round respondership (RR) and respondership (RC).
δ
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
26
1
1
2
3
4
5
6
7
8
9
10
11
12
2
3
4
5
6
^y
yi
d
u
^y
yi
d
u
^y
yi
d
u
^y
yi
d
u
^y
yi
d
u ^y yi
u
30
25
20
20
50
20
15
15
25
25
20
20
20
21
20
23
10
30
20
25
30
20
20
25
23
20
27
49
25
27
20
0
20
24
20
35
25
20
25
28
27
10
25
25
20
20
20
25
26
25
24
25
25
20
25
25
20
25
23
20
23
20
15
15
9
0
20
8
10
20
25
5
0
10
12
30
15
10
25
13
1
20
1
15
18
10
1
12
24
9
10
0
0
10
20
15
20
1
8
25
30
25
10
15
24
23
19
17
17
20
1
15
0
0
1
1
0
26
15
21
0
13
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
25
0
25
0
0
0
0
20
0
0
0
0
0
0
0
25
0
26
0
0
0
21
0
0
0
0
0
20
0
0
0
0
20
0
0
0
0
20
0
0
0
0
0
0
0
20
0
10
0
0
0
25
0
0
0
0
10
25
15
9
50
35
10
22
25
25
10
20
20
15
30
15
10
25
20
25
15
20
25
15
20
25
5
49
12
25
15
10
15
35
10
30
15
15
25
32
22
15
20
23
30
15
15
20
20
10
15
40
25
15
30
20
20
20
25
10
21
10
0
10
9
0
10
1
1
5
1
0
0
10
9
30
10
2
16
1
0
12
1
20
8
1
0
2
0
5
1
0
0
5
15
1
0
0
0
5
21
20
15
5
20
31
9
10
12
15
1
8
0
0
0
0
0
19
5
24
0
7
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
20
0
0
0
0
0
0
0
10
17
0
0
0
0
0
0
0
0
15
0
0
0
0
23
0
0
20
0
0
18
0
0
0
0
15
0
0
0
0
0
0
25
0
0
0
0
0
0
20
0
0
0
10
0
20
0
0
0
0
5
20
7
10
5
25
10
30
25
10
2
15
20
10
40
40
10
6
20
25
10
10
20
15
18
20
25
49
10
20
15
0
25
5
15
25
10
5
25
36
25
10
20
25
30
32
10
27
15
20
10
10
25
7
1
10
15
34
30
0
17
8
0
5
5
25
20
5
0
0
0
0
0
1
0
10
4
0
3
0
0
6
0
5
2
0
0
20
0
1
0
0
0
1
0
10
0
1
15
3
18
1
5
4
10
25
15
5
1
10
1
0
0
25
0
0
0
13
10
7
10
5
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
15
0
0
0
0
0
5
0
0
0
15
0
0
0
0
0
0
10
0
0
21
0
0
0
0
0
0
0
15
0
0
0
20
0
12
0
0
0
0
22
0
0
0
0
0
0
0
0
15
0
0
0
10
0
15
0
0
0
0
10
10
5
2
25
5
15
10
25
10
10
10
20
0
25
33
35
6
20
10
6
30
5
16
23
20
25
1
0
30
13
0
10
10
15
10
40
5
25
13
25
10
10
30
25
10
10
3
10
10
8
0
10
7
1
10
10
27
40
0
14
8
0
2
2
0
14
5
0
0
0
0
0
0
0
5
4
0
1
0
0
4
0
3
0
1
0
25
0
0
0
0
0
10
0
2
0
0
1
1
13
1
1
0
10
5
1
4
0
10
20
0
25
0
0
0
24
8
1
0
10
4
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
0
0
8
0
0
0
10
0
0
8
0
0
0
0
0
0
13
0
14
0
0
0
0
0
15
0
0
0
10
0
0
0
0
0
0
20
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
10
0
15
5
5
0
25
1
20
45
0
7
0
5
20
0
30
39
50
1
20
1
4
13
5
12
3
15
25
1
20
15
7
10
5
20
1
10
5
0
20
2
25
10
15
25
11
20
5
10
5
8
10
10
50
5
1
0
4
19
35
10
13
5
10
0
0
0
0
8
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
15
0
0
0
0
0
5
0
0
0
0
0
1
2
1
0
0
5
0
0
5
0
10
0
0
0
40
0
0
1
2
5
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
0
0
5
0
0
0
0
0
0
7
0
0
0
0
0
8
0
0
0
0
11
0
0
0
0
0
12
0
12
0
0
0
0
0
18
0
0
0
0
0
0
15
0
10
0
0
0
0
0
0
0
10
25
25
25
25
25
6
6
6
0
6
20
20
20
20
20
14
14
14
14
14
20
20
20
20
20
27
27
27
27
27
20
20
20
20
20
15
15
15
15
15
25
25
25
25
25
15
15
15
15
15
20
20
20
20
20
20
0
20
20
20
18
Table G.2: The offer expectations ( y$ ) acceptance thresholds ( y i ) of responders and
their decisiveness (d) as well as their payoff (u) for all 6 rounds without
responder competition (RR).
25
25
5
17
30
25
15
20
25
25
5
25
20
0
19
9
50
20
0
25
8
10
0
16
1
20
2
50
20
20
15
35
1
0
0
20
0
1
10
1
25
10
10
20
15
18
8
19
26
10
18
25
25
15
1
20
25
20
30
20
16
2
23
0
15
0
5
5
0
20
0
0
0
0
0
5
8
0
0
0
0
6
0
0
0
1
5
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
10
5
1
15
4
0
0
0
10
0
20
22
9
10
10
4
27
1
1
2
3
4
5
6
7
8
9
10
^y
yi
d
u
^y
yi
2
d
u
^y
yi
3
d
u
^y
yi
4
d
u
^y
yi
5
d
6
u ^y yi
u
1
1
0
0
49
1
0
0
10
1
0
0
1
1
0
0
1
1
0
0
20
1
1
49
1
0
0
29
21
1
25
28
22
0
0
49
1
0
0
29
21
1
25 30
20 20
1
5
0
0
25
49
0
0
10
10
0
0
18
25
0
0
5
6
0
0
12 20
20
15
0
0
35
15
0
0
25
5
1
25
27
5
1
25
27
5
0
0
15
5
25
25
1
35
45
20
0
0
20
1
0
0
25
25
0
0
25
15
0
0
25
10 20
19
20
35
5
1
21
20
0
0
0
25
0
0
0
30
0
0
0
15
0
0
0
40
0
6
25
0
0
0
25
0
0
0
49
0
1
15
15
0
0
0
49
0
0
0
25
0
6
8
6
0
0
10
7
0
0
10
7
0
0
9
8
0
0
9
8
0
0
25
20
0
25
0
0
0
9
8
1
22
9
8
0
0
25
0
1
10
25
1
1
5
25
1
6
19
13
0
0
10
1
0
0
20
15
0
0
50
25
0
0
26
0
0
0
35
25
0
30
0
1
10
30
20
0
0
25
25
0
0
25
25
1
25
25
25
0
0
25
25
0
15
5
0
0
15
5
0
0
10
5
1
20
10
5
0
0
10
5
0
0
10
5
10
49
15
0
0
5
10
1
30
15
10
0
0
10
10
0
0
5
5
0
0
5
5
10
25
20
0
0
20
20
0
0
25
15
0
0
25
10
0
0
25
15
0
0
15
10 10
0
0
0
0
20
10
0
0
25
24
0
0
10
5
0
0
40
30
1
0
20
1
25
21
1
22
24
21
0
0
22
18
0
0
22
18
0
0
22
20
0
0
22
20 26
10
10
10 26
10
0
0
0
0
0
0
0
0
0
10
0
0
0
30
26
0
0
30
24
0
0
24
1
0
0
24
30
10
0
0
24
10
1
18
27
15
0
0
27
25
20
0
0
24
19
0
0
15
1
1
15
25
1
0
0
25
1
0
0
9
1
26
25
25
1
0
24
20
0
0
24
20
0
0
24
20
0
0
24
20
0
0
20
1
25
30
20
0
0
50
13
0
0
25
25
0
0
30
20
1
26
33
20
0
0
25
0
25
25
20
0
0
20
15
1
27
20
15
0
0
15
10
0
0
20
15
1
22 19
25
20
0
0
25
20
0
0
25
10
0
0
25
5
0
0
15
10
0
0
1
1
21
20
0
0
24
18
0
0
24
15
1
28
25
14
0
0
25
16
0
0
26
14 25
20 30
17
1
15
0
10
0
0
0
0
24
1
1
10 25
1
26
0
0
25
9
0
0
5
26
22
15 25
25
10
5
1
37
50
0
0
0
14
3
0
0
40
2
0
0
50
0
1
20 25
25
10
0
0
20
1
0
0
30
1
0
0
15
1
1
21
30
1
0
0
25
1
30
50
23
0
0
50
27
1
30
50
32
0
0
50
36
0
0
50
40
0
0
50
0
30
23 30
5
45
0
0
15
35
0
0
25
25
1
27
32
18
0
0
12
38
0
0
27
30
15
0
0
35
10
0
0
25
10
0
0
30
10
0
0
40
10
0
0
30
5
25
20
1
20
25
20
0
0
25
20
0
0
25
20
1
0
25
20
0
0
25
20 20
22
17 20
30
23
20
0
0
18
15
0
0
20
15
1
15
22
18
0
0
20
15
0
0
25
20
0
0
25
20
0
0
25
20
0
0
25
20
0
0
25
20
1
20 13
7
20
17
0
0
25
20
1
20
20
20
0
0
25
15
0
0
20
10
0
0
15
10 20
20
12
10
0
0
30
20
0
0
14
12
0
0
8
6
0
0
18
17
0
0
22
22
0
25
20
0
0
25
1
0
0
25
1
1
25
25
1
0
0
25
1
0
0
25
1
15
25
1
0
0
30
1
1
20
22
1
0
0
25
1
0
0
20
1
0
0
20
1
15
23
7
0
0
3
2
0
0
25
1
0
0
5
1
0
0
14
1
1
22 20
1
15
20
20
1
27
25
10
0
0
15
5
0
0
10
2
0
0
10
2
0
0
10
5
15
26
1
0
0
26
1
0
0
26
1
0
0
26
1
1
18
26
1
0
0
8
1
15
10
15
0
0
25
25
0
0
10
1
1
20
10
1
0
0
5
1
0
0
25
1
20
20
15
0
0
22
18
0
0
17
15
0
0
17
10
0
0
10
5
0
0
25
15 20
10 20
25
0
1
25
25
0
0
0
25
0
0
0
25
0
0
0
25
0
0
0
20
25
20
0
0
25
1
0
0
25
1
0
0
25
1
0
0
25
1
0
0
20
1
20
10
20
0
0
25
10
1
0
5
5
0
0
1
25
1
0
1
48
0
0
1
1
20
20
20
0
0
20
15
0
0
15
15
0
0
15
0
0
0
15
0
0
0
15
10 25
10
9
0
0
20
25
1
0
26
25
0
0
30
29
0
0
30
20
0
0
20
15 25
20
20
0
0
20
10
0
0
20
10
0
0
20
10
1
10
20
15
1
25 10
10 25
15
25
0
0
10
20
0
0
22
15
1
25
15
20
0
0
20
20
0
0
10 25
25
1
1
25
25
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
22
13
24
13
21
11
21
10
21
11
25
1
1
25
20
8
19
Table G.3: The offer expectations ( y$ ) acceptance thresholds ( y i ) of responders and their
decisiveness (d) as well as their payoff (u) for all 6 rounds of responder
competition (RC).
28
Table G.4 : Answers to the control questions : questionnaire 1 (AT1) question 1 (A11),
question 2 (A22) and questionnaire 2 (AT2), question 1 (A21) and question 2 (A22) and
both questionnaires (A).
RR
RC
AT1 AT2 ATT AT1 AT2 ATT
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
40 38
33
1
1
1
1
1
1
0
1
0
1
1
1
ATi= 1 (or 0) - (not) all answers of i.
1
1
1
1
1
1
control questionnaire are correct
0
1
0
ATT=1 (or 0) - (not) all answers of both
1
1
1
1
1
1
control questionnaires are correct
1
1
1
44 52
40
RR
RC
AT1 AT2 ATT AT1 AT2 ATT
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
7
7
1
1
1
1
1
1
12
10
10