The data used for this article can be accessed online at http://datadryad.org/, doi:10.5061/dryad.tp582. We are happy to provide more information on request.
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APPENDIX to Chapter I: Electronic Supplementary Material (ESM)
The Prisoner’s Dilemma Game cooperates, the defector receives the temptation payoff (T) and the cooperator obtains the sucker’s payoff (S). However, if both defect, they each receive the punishment payoff (P). The assumptions T > R > P > S must hold (and if the game is repeated 2R >
T + S):
[1]
If the individuals cooperate, both do better than if they had both defected (R > P). For a single individual, it is always better to defect no matter what the partner does (T > R and P > S). It is clear that under these simple rules, only defection can be evolutionarily stable. In other words, cooperative behaviour is vulnerable to exploitation in one-shot interactions. However, the dilemma can be resolved in repeated interactions by direct reciprocity: “If you help me, I will help you next time”. It has been shown that cooperation can evolve if the probability of another round is high enough and that humans use direct reciprocity to establish cooperation.
(A) decisonsPD feedbackPD
(B) decisonsPD feedbackPD breaking link-decisions
link-breaking feedback
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Figure S1. Decision and feedback diagram of one round. Participants played prisoner’s dilemma (PD) games with three partners (STATIC, panel A) or could break social links and receive new partners at random in either dynamic-network treatment. Setting new links was cost-free (DYNAMIC, panel B) or else low costs of 0.10€ (DYNAMIC10, panel C) or high costs of 0.50€ (DYNAMIC50, panel C) arose. For the PD decision, participants were asked “Do you want to play ‘orange’ or ‘blue’ ?” (orange-/blue-buttons, see methods for details). For a link-breaking decision they were asked “Do you want to keep playing with this partner in the next round?” (yes-/no-buttons). If there were open links they were asked for a link-making decision “Do you want to receive a random new partner for costs of 10 [50] cents?” (yes-/no-buttons).
Screenshots: decision making during the experiment
During the experiment participants were confronted with different decisions. In the STATIC treatment participants saw Fig. S3 and Fig. S4 (however, no decisions could be made in the latter case). Additionally, in the DYNAMIC treatment participants saw Fig.
S5a and in DYNAMIC10 and DYNAMIC50 treatments they saw Fig S5b.
Figure S3. In the prisoner’s dilemma game, participants were asked whether to play
“orange” (orange, in this particular case cooperation) or “blau” (blue, defection) and had to make one decision for every linked partner.
(C) decisonsPD feedbackPD
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Figure S4. Participants were provided with the outcome of the prisoner’s dilemma decisions (the third column indicates the participant’s payoff and the fifth column the partner’s payoff). In the link-breaking stage of the dynamic treatments participants were asked whether to continue playing with a partner and could answer “ja” (yes) or “nein”
(no). They had to make one decision for every linked partner.
Figure S5a. In the DYNAMIC treatment participants were provided with a summary of the link-breaking decisions. Here, the participant continues to play with Rhea (pseudonym); Dione declined to keep playing with the participant; and in the case of Nereid the participant declined to continue the relationship. Thus, the participant would receive two new, randomly chosen partners.
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Figure S5b. In the DYNAMIC50 (DYNAMIC10) treatment participants were also provided with a summary of the link-breaking decisions. In addition, for each broken link, participants must decide whether they wish to seek a new partner at a cost of 0.50€
(0.10€), i.e. answer “ja” (yes) or “nein” (no).
Table S1. Statistical test details of differences in the link-breaking rate between each of the three dynamic-network treatments where no (DYNAMIC), low (DYNAMIC10), or high costs (DYNAMIC50) arose for receiving new links.
χ2 / W n df p
general test: Kruskal-Wallis test
21.17 10 2 < 0.001
multiple comparisons with Wilcoxon rank-sum test (3 tests)
DYNAMIC vs. DYNAMIC10 0 10 < 0.001
DYNAMIC vs. DYNAMIC50 0 10 < 0.001
DYNAMIC10 vs. DYNAMIC50 17 10 < 0.05
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Figure S2. Average cooperation rates over rounds. Participants played prisoner’s dilemma games with three partners. Those partners were either fixed (STATIC) or participants could break social links after each round. In the latter case, setting new links was either cost-free (DYNAMIC), or else low costs of 0.10€ (DYNAMIC10) or high costs of 0.50€ (DYNAMIC50) arose.
0 % 10 % 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 % 100 %
1 6 11 16 21 26
cooperation rate
rounds
STATIC DYNAMIC DYNAMIC10 DYNAMIC50
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Table S2. Statistical test details of differences in the average cooperation level in the prisoner’s dilemma games of the static-network treatment (STATIC) and the three dynamic-network treatments where no (DYNAMIC), low (DYNAMIC10), or high costs (DYNAMIC50) arose for receiving new links.
χ2 / W n df p
general test: Kruskal-Wallis test
16.23 10 3 < 0.01
multiple comparisons with Wilcoxon rank-sum test (6 tests)
STATIC vs. DYNAMIC 4 10 < 0.001 participant received a newly linked partner in the dynamic-network treatments where no (DYNAMIC), low (DYNAMIC10), or high costs (DYNAMIC50) arose for receiving new links.
χ2 / W n Df p
general test: Kruskal-Wallis test
12.42 10 2 < 0.01
multiple comparisons with Wilcoxon rank-sum test (3 tests)
DYNAMIC vs. DYNAMIC10 25 10 0.06
DYNAMIC vs. DYNAMIC50 10 10 < 0.01
DYNAMIC10 vs. DYNAMIC50 31 10 0.16
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Table S4. Statistical test details of differences in the willingness of participants to reciprocate defection in the three dynamic-network treatments where no (DYNAMIC), low (DYNAMIC10), or high costs (DYNAMIC50) arose for receiving new links.
χ2 / W n df p
general test: Kruskal-Wallis test
12.95 10 3 < 0.01
multiple comparisons with Wilcoxon rank-sum test (3 tests)
DYNAMIC vs. DYNAMIC10 11 10 < 0.05
DYNAMIC vs. DYNAMIC50 31 10 0.17
DYNAMIC10 vs. DYNAMIC50 64 10 0.32
45 Additional figures of conditional behaviour
(a) (b)
(c) (d)
Figure S6. The x-axis shows behaviour of both partners in the previous round, i.e. CC means both players played C, CD means one player played C, the other player D, etc. In case the link between the two players was not broken, the plots show the frequency of actions in the following round. For example, in DYNAMIC treatment (a), if both players played C and kept the link, then in the following round they both played C in 93,65% (orange bar) of the cases. Similarly for DYNAMIC10 (b), DYNAMIC50 (c) and STATIC (d). This picture does not reveal how often links were kept and who of the players decided to break the link (cf. Fig. S7.)
0%
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(b)
(c)
Figure S7. The x-axis shows behaviour of both partners in the previous round. The plots show the frequency of all possible bilateral actions of the players in the following round: BB, if both players decided to break the link, BK or KB, if one player decided to break the link and the other player decided to keep it. If both players decided to keep the
0%
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link (KK), their actions in the following prisoner’s dilemma game can be DD, DC, CD or CC. Because all links are automatically kept in the STATIC treatment, it is already covered in Figure S6d.
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