SUPPLEMENTARY INFORMATION
Reputation-based cooperation: empirical evidence for behavioral strategies
V. Swakman, L. Molleman, A. Ule and M. Egas
CONTENTS
S1. Supplementary Figures
S2. Additional statistics
S3. Experimental procedures and instructions
S4. Screenshots of the decision-making environment
Section S1. Supplementary Figures
Supplementary Figure 1. Dynamics of helping over the rounds of the game.Panels show helping rates for each of our three experimental conditions. Gray lines show 10-round average helping ratesforeach of the replicate groups over the course of the game. Colored symbols show averages across groups for each condition. To test for changes in helping rate over the rounds in each of the conditions separately, we fitted logistic generalizedlinear mixed models to helping decisions. We used as fixed factors ‘round’ and a dummy variable for the last 10 rounds (to account for the end-effect in our finitely repeated game), and as random factors ‘subject nested in group’. These models detect strongly negative effects of the round number (z< –8.140; P<0.001) in both the CONTROL and the COSTLY condition, but no effect of round in the FREE condition (z=0.134; P=0.432).
Supplementary Figure 2. Aggregate responses to first-order information and second-order information on defection. Panels show helping rates based on 1st-order and, when available, 2nd-order information; (a-d): CONTROL; (e-h): FREE; (i-l):COSTLY. Dotted horizontal lines show mean helping rates of donors for each degree of helpfulness of their recipients when2nd-order information was unavailable or not requested; transparent bands indicate ±1 SE. In each treatment, recipient’s helpfulness increases from the left panels to the right panels (numbers on top indicate the number of GIVE decisions out of the most recent three). Within panels (e-g)and (i-k), connected dots display helping rates (± 1 SE) as a function of the helpfulness of the recipient’s recipient, when 2nd-order information was requested on a DENY decision. Connected dots tend to decrease as a function of 2nd-order information, possibly reflecting effects of reasons behind defection: help is directed towards those who denied help to selfish individuals (Table 1, column 2). For comparison, mean helping rates are given for those cases where 2nd-orderinformation on a DENY decision was absent (CONTROL treatment; panels a-d), or not available (cases where 1st-order information on the recipient showed three times ‘GIVE’ and no ‘DENY’; panels h and l).
Supplementary Figure 3. Aggregate responses to first-order information and second-order information on cooperation.On average, help tends to bechanneled to those recipients that help cooperators (panels as in Fig S2). Responses to 2nd-order information ondecisions to GIVE help decisions are less pronounced than responses to such information on decisions to DENY help. In panels g and h, connected dots tend to increase as a function of 2nd-order information, possibly reflecting effects of reasons behind helping: help is directed towards those who gave help to cooperative individuals (Table 1, column 3).
Supplementary Figure 4.Helping behavior of all common strategies identified by our classification procedure. Panels show mean responses to 1st-order information and, when significantly affecting helping decisions,responses to 2nd-order information and/or own reputation (+/- 1 SE). Roman numerals correspond to strategies indicated in Figure 2 of the main text. Axes are as in Figure 3 of the main text. The number of individuals falling into each category is indicated at the top left of each panel. In total, we classified 131 out of the 160 participants. Two strategies (cf. Figure 2 segments v, vi) are not shown here because they contained fewer than 5 individuals. Most strategies do not differ in their performance in the experiment: we only observe that the few unconditional cooperators tended to achieve relatively low payoffs (Tukey-Kramer tests on linear mixed model fitted to weighted average payoffs in the roles of donor and recipient: P=0.042 and 0.048 compared to unconditional defectors and first-order conditional cooperators, respectively; P > 0.15 for every other pairwise comparison).
Section S2. Additional statistics
Requesting 2nd-order information
Figure 1 of the main text shows the distribution of requests for 2nd-order information. To assess the effects of information cost and the extremeness of 1st-order information (i.e., the helpfulness of recipients), we first coded the helpfulness of recipients as ‘intermediate’ (chose to GIVEhelp 1 or 2 times out of the most recent three actions), or ‘extreme’ (chose to GIVE help 0 or 3 times out of the most recent three actions). Subsequently, we fitted a logistic generalized linear mixed model to individual decisions to request 2nd-order information, including ‘information cost’ (FREE or COSTLY) and ‘helpfulness of recipient’ (intermediate or extreme) as fixed factors, and ‘subject’ as random factor. This model detects a strong negative effect of information cost (P<0.001), indicating that requests for 2nd-order information are significantly more frequent when free. We also observe a strong effect of the extremity of recipients’ helpfulness on information requests (P<0.001): requests are significantly more frequent when 1st-order information shows intermediate levels of helpfulness.
Responding to 2nd-order information
The aggregate responses to 1st- and 2nd-order information are summarized in Table 1 and further illustrated in Figures S2 and S3. Eyeballing the responses to 2nd-order information in FREE versus COSTLY in those figures suggests that 2nd-order information has a stronger effect when requesting it was costly (compare the slope of the dotted lines in Figure S2f and S2j, and S2g vs S2k). Indeed, a logistic linear model fit to those decisions where donors requested 2nd-order information on ‘DENY’ decisions of their recipients detects a significant interaction effect between “experimental condition” and “helpfulness of the recipient’s recipient”.
Effects on average cooperation levels
Given the stronger impact of 2nd-order information when it was costly to request, one mightwonder why cooperation tends to be more stable in the FREE condition, compared to the COSTLY condition (see Supplementary Figure 1). This observation may be partly explained by the fact that that in the FREE condition, overall information request rates were higher (see Figure 1 of the main text), and, correspondingly, the prevalence of strategies using 2nd-order information detected by our classification was higher (Figure 2 of the main text; Fisher-exact test: P=0.015).
Section S3. Experimental procedures and instructions
Experimental procedures
Experimental conditions were divided over two locations in The Netherlands (University of Amsterdam: 4x CONTROL, 2x FREE, 4x COSTLY; University of Groningen: 4x FREE, 2x COSTLY). Subjects were mostly undergraduate students from the social sciences, economics and biology. Sessions lasted around 90 minutes. Subjects received a show-up fee of €7 and on average earned €14.44 on top of that according their performance. In the reception room, participants drew a card with a number corresponding to a desk in the computer laboratory. Once the subjects had entered the laboratory, they were no longer allowed to communicate. Paper instructions in Dutch (see below for English translation) were distributed and read out loud by one of the experimenters. Before the experiment itself started, subjects had to fill out a brief quiz to check their understanding of the experiment. Sessions finished with a questionnaire including items about personal demographic background. Finally, subjects were paid individually in the reception room.
Instructions
For each of the three experimental conditions, instructions were largely identical, but differed with respect to the availability (and costs) of 2nd-orderinformation. In the text printed below, we will indicate which parts are identical for each experimental condition and which parts are specific to either of them. Original instructions were in Dutch, the text below is a translation.
=== Instructions ===
Introduction
Welcome to this experiment on decision making. The experiment lasts for about 90 minutes. During the session you are not allowed to talk or communicate with the other participants. If you have a question, you can raise your hand and one of us will come to you to answer it.
During the experiment you will make money. Your earnings depend on your decisions and the decisions of others. At the end of this session, the money you earned, plus a 7 euro show-up fee, will be paid to you in cash. These payments are anonymous; you will be paid individually in the reception room. After the experiment has ended, please remain seated until we call you desk number. None of the other participants will be informed of your earnings. We cannot connect your desk number to your identity. You start out with 3000 points, and 300 points are worth 1 euro.
Setup of this session
- Instructions
- Quiz to check if you understand the experiment
- The experiment itself
- Questionnaire
- Payment
The experiment consists of 100 rounds and takes place in groups of 10. In each round, you will be paired with one of the nine other participants in your group. Everyone remains anonymous; you will not receive information about the identity of the participant you are paired with.
In each round again, a role (A or B) is randomly assigned to you. You only have to make a decision when you are assigned role A. When you are assigned role B, you do not have to do anything.
Making decisions
When you are assigned role A, you can choose between two alternatives. When you choose ‘blue’, player B that is paired with you received 250 points. You lose 200 points. When you choose ‘purple’, the player that is paired to you receives nothing, and you do not lose any points.
In summary:
Blue costs Participant A 200 points. Participant B receives 250 points.
Purple yields 0 points for both.
=== The following part was specific to the condition where 2nd-orderinformation was not available (CONTROL) ===
Information
When you are making your decision, the screen will show the three most recent decisions that the participant in role B has taken, when he was in the role of A.
These three decisions of the participant in role B are displayed in three boxes on your screen. These boxes are given in random order. When B has not yet been in the role of A, you will see a “-“.
=== The following part was specific to the conditions in which 2nd-orderinformation was available (COSTLY and FREE). We use square brackets to indicate where instructions differed between the two [with information specific for the COSTLY treatment in brackets] ===
Information
When you are taking your decision, you have two sorts of information at your disposal.
- Your screen will display the three most recent decisions that the participant in role B has taken, when he was in the role of A. These three decisions of the participant in role B will always be displayed to you, and displayed in three boxes on your screen. These boxes are given in random order. When B has not yet been in the role of A, you will see a “-“.
- About one of these three decisions of the participant with role B, you can request additional information.
If you select the option ‘additional information’ under one of the decisions, the information that B had, when he made this decision will be shown to you. This information consists of the three most recent decisions of the participant with which B was paired at that time. These decisions are also given in random order. You can confirm your decision by clicking the button ‘Continue’. [ Viewing this information is costly. It costs 5 points to view it. ]
NB: you can request additional information for only one of the decisions of the participant with role B. If you select ‘additional information’ for more than one decision, an error message will appear on your screen.
In summary:
Always available: the most recent three decisions of participant B
Optionally available [ at a cost of 5 points ]: additional information on one decision of participant B, namely the three most recent decisions of the participant with which B was paired at that time.
=== the rest of the instructions were identical for each of the experimental conditions ===
The end of a round
When participant A has made his decision, both participants are informed about their score in this round, and their total amount of points at that moment. This is the end of the round. You will be paired to a new participant. Randomly, you will be assigned the role of A or B.
The end of the session
When the experiment has ended, a questionnaire will follow.
Please remain seated after filling out the questionnaire, until we call your desk number. You will be paid individually in the reception room.
Section S4. Screenshots of the decision-making environment
Screenshot A. The decision-making environment. The donor decides whether or not to request 2nd-orderinformation. The boxes contain the most recent decisions of the recipient (in random order). The blue (Dutch: ‘blauw’) option refers to a GIVE decision, and thepurple (Dutch: ‘paars’)option refers to a DENY decision. Donors could check a box below one of these decisions and click the red button on the far right side of the screen, after which 2nd-orderinformation on that decision was displayed to the donor (see Screenshot B below). In the CONTROL condition subjects could not request 2nd-orderinformation, and the checkboxes were absent.
Screenshot B. Displaying 2nd-orderinformation.In this case, the donor has requested 2nd-orderinformation on a ‘purple’ (DENY) decision. The 2nd-orderinformation associated with that decision is printed below the box (again in random order). On the far right of the screen, the donor can make his decision and confirm it by clicking the red button.
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