Modelling pandemic behaviour using an economic multiplayer game | Scientific Reports – Nature.com


Participants

The final sample consisted of 134 participants: 57 (42.5%) males, 76 (56.7%) females, and 1 (0.7%) indeterminate/intersex/unspecified with a mean age of 35.5 (SD = 12.0). Participants were required to be fluent in English, residents of the UK. Participants were excluded before completion of the experiment if they were diagnosed with dyslexia, dyspraxia, attention deficit hyperactivity disorder, or if they had trouble reading for any reason (including uncorrected abnormal vision).

The data collection was completed between 20 and 23 January 2021 via the Prolific online research participant database. At this stage in the COVID-19 pandemic, the UK was on the cusp of 100.000 COVID-related deaths, and two weeks earlier the National Health Service (NHS) England’s national medical director urged people to physically distance because the NHS was under extreme pressure. The country was in lockdown without a clear end date. In addition, 3.07% of participants reported they had received a positive COVID-19 diagnosis.

The experiment was divided into 14 sessions with 11 participants each, for an initial total of 154 participants. The minimum group size after exclusions per session was eight. Any sessions that did not meet the cut-off were excluded from data analysis. 20 participants were excluded, most of whom dropped out while waiting for the experiment to start (19), 1 participant provided low effort data by missing too many responses. We departed from the preregistration here. We stated that we would discard data on a particular DV for participants who provided the same responses in 95% of the rounds for that DV. Seeing as there are legitimate reasons to respond the same each round, we did not go through with this exclusion procedure. Instead, if participants’ pages timed out in 30% of the rounds or more, their data was excluded.

Participants were paid £2.00, with a bonus of £0.20 for every 100 points (the endowment for each round). There were 40 rounds, so participants could accrue a maximum of £10. All participants provided informed consent as approved by the Monash University Human Research Ethics Committee (Project ID: 26499).

Apparatus

This experiment was an online study, and participants were asked not to use mobile devices. No default options were used for any of the questions, and the options were always presented left to right in increasing order to avoid any confusion. The pages had timeout timers that would only appear when time was running out. This was done to streamline the experiment and make long waiting times unlikely while limiting the effect on the participants.

Procedure

Participants began the study by completing a short questionnaire, stating their age, their sex, whether they had tested positive for COVID-19 in the past, and in which region within the UK they resided (i.e., England, Scotland, Wales, or Northern Ireland). Further, as an attention check, they were asked which city was not a city in the US, with the list including Tokyo, but with a subheading that read: “Regardless of the right answer, please select Chicago”. The attention check was not preregistered, but was added to flag submissions for more careful review. We could not find any reason to exclude the participants who failed the attention check, and found that excluding them would make little difference to the results (see Supplementary Materials for additional information, and a secondary analysis without these participants in the sample). Afterwards, they were presented with an introduction and instructions on how to play the game, which was created using oTree31.

Participants were made aware that a randomly selected player in the group was infected with COVID-19 and that they could spread it to other players in the group. They did not know who this ‘patient zero’ was, and were told that they could be patient zero themselves. Additionally, they would not know whether they were infected at any point, nor would they experience a decrease in income if they got infected. When six players were infected with the virus, the group would go into lockdown for two rounds, costing either 60 or 90 points per round, in the Low Cost and High Cost conditions, respectively. After a lockdown, a new patient zero was randomly selected. Players were notified that they were playing to get points and that to do this they could avoid lockdowns by reducing viral transmission through self-isolation (see instructions here https://osf.io/tr6y3/?view_only=aa314332c12c45548484ac084feed2f0).

In each round, the game required several responses from the participants; if one of the pages timed out before they responded, they were not paid for the round. First, we implemented a variation to the strategy method: to see how players would respond to different levels of self-isolation in the group, players were asked “If you knew what the average self-isolation level of the others in the group was in this round, how much would you self-isolate?”, with five sub-questions reading: “If the group self-isolation average were—[insert level]”. Thus, each of these sub-questions presents a different hypothetical scenario (hereafter: others’ self-isolation in scenario). For each sub-question, the response could be one of 5 self-isolation levels: not at all, slightly, moderately, stringently, or completely (hereafter: hypothetical self-isolation). Second, participants would provide their response to “On average, how much do you think others will self-isolate in this round?”, choosing one of the aforementioned options (hereafter: beliefs about others’ behaviour). Last, they answered: “How much do you actually want to self-isolate in this round?”, emphasising that this response would be incentivised (hereafter: incentivised self-isolation, see below). See Fig. 1 for the flow of the experiment from the participants’ point of view.

Figure 1
figure 1

A trial-level schematic of the game from the players’ point of view.

Participants’ endowment was 100 points in each round and they could sacrifice a part of their income by selecting one of the following options: sacrifice no points by choosing the self-isolation level “Not at all”, sacrifice 10% (i.e., 10 points) to slightly self-isolate, 20% to moderately self-isolate, 30% to stringently self-isolate, or 40% to completely self-isolate. Participants were not made aware of how much the self-isolation would decrease the chance of transmission (because this is also not the case in the real world).

The transmission chance was determined through a stochastic process: if an infected player and a healthy player would not self-isolate at all in the same round, then the chance of transmission would be 100%, while if one of them would self-isolate moderately, this would be reduced to 50%. For example, if an infected player would self-isolate moderately, but a healthy player would not self-isolate at all, then the chance of the infected player transmitting the virus to the other player would be 50%. See Fig. 2 for the dynamics of transmission and the by-trial process.

Figure 2
figure 2

The costs and a demonstration of the viral transmission in the game. Participants all get 100 points of endowment in each (non-lockdown) round. They are then given a chance to choose their level of self-isolation to a maximum of 40% of their income, leaving minimally 60 points. This case depicts a scenario with only one infected player who does not self-isolate at all (at the bottom of the group, in red). Players who aren’t yet infected and do not self-isolate at all have 100% chance of getting infected, whereas players who self-isolate moderately (20% of endowment sacrificed) have 50% chance to get infected. The different self-isolation levels are indicated by differences in circles around the players (e.g., the green solid line is complete self-isolation (40% of endowment sacrificed), the dark orange dashed circle is slight self-isolation (10% of endowment)).

Participants were all subjected to both lockdown cost conditions, and the order of presentation was counterbalanced. After 20 rounds in the initial lockdown cost condition, halfway through the experiment, either High Cost or Low Cost, participants were shown a message stating the new lockdown cost regime. The Low Cost condition was set to 60 points because it would equate incomes of groups where every member is completely self-isolating (i.e., for three rounds: 3*60 points), and not self-isolating at all (i.e., for three rounds: 100 points + 2*40 points in lockdown). The High Lockdown Cost condition was chosen to provide a strong contrast to this situation where not self-isolating resulted in efficiency loss; providing only 2/3 of the income of a fully self-isolating group (100 + 2*10). The range of outcomes for participants was, then, £4.98 (complete self-isolation and maximum number of lockdowns) and £10 (no self-isolation and no lockdowns).

After players entered their choices, they were presented with essential information regarding the results of that round. Specifically, they were shown: how much they had earned (i.e., endowment—self-isolation cost, or lockdown endowment); average self-isolation of others, as a percentage of complete self-isolation; how many infected players there were, and how many players there were in the group; their cumulative earnings in points. The presented information during the various participant inputs was held constant, and so participants were always shown how many infected players there were in the group, and what the cost of a lockdown would be if it were to occur after that round. For further details of the procedure, see Supplementary Materials.

Analysis

Simulations

To compare participants’ behaviour to profit maximising strategies we simulated the income generated by adopting different strategies along the empirical boundaries of the game. We vary other players’ cooperativeness from complete defection (all other players select ‘no self-isolation’ in each round), to complete cooperation (all other players select ‘complete self-isolation’ in each round). We first simulated the game’s outcomes for the five possible static strategies, where the fictional player of interest maintains the same level of self-isolation throughout the game, among the changing environment of the other 10 players’ cooperativeness. For all strategies, income drops strongly as others become less cooperative. However, under both levels of lockdown cost, and the different levels of cooperativeness of the group, less self-isolation is more profitable.

In addition, we modelled the performance of dynamic strategies whereby players increase or decrease their level of self-isolation when infections rise. The fictional player of interest starts by choosing moderate self-isolation in every round but will either increase their self-isolation to complete self-isolation (‘Moderate to Complete’ strategy), or decrease it to no self-isolation (‘Moderate to None’ strategy) when there are more than two infections in the group. We compare this to the static ‘Moderate Cooperator’ strategy, where the player always chooses moderate self-isolation in each round.

Preregistered analyses

Based on the within-subjects design with only one manipulated variable (lockdown cost, with two levels), and various observed variables, we opted for a linear mixed modelling approach, which allowed for the controlling of the dependence between observations. There were three dependent variables (DV): incentivised self-isolation, hypothetical self-isolation, and beliefs about others’ behaviour. There were three other independent variables (IV) of interest: the cost of lockdown, the number of infections in the group, and the self-isolation of others in hypothetical scenarios. Other observed variables were used as control variables, these were: the round in which the observations were made and the average self-isolation of others in the previous round.

A linear mixed model (LMM) was used to analyse the effects of the number of infected players (H1) and beliefs about others’ self-isolation (H3a) on incentivised self-isolation. In this model, the DV was incentivised self-isolation, and the IVs were the number of infections, the self-isolation of others in the previous round, people’s beliefs about others’ self-isolation, and the round number. The model included participants as a random intercept and the round number as a random slope.

Another LMM was used to analyse the effects of the number of infections on beliefs about others’ self-isolation (H2). In this model, the DV was beliefs about others’ self-isolation, the IVs were the round number, the number of infections, the self-isolation of others in the previous round. The model also included the participants’ IDs as the random intercept and the round number as the random slope. A third LMM was used to analyse the effects of others’ self-isolation in a scenario on self-reported hypothetical self-isolation (H3b). In this model, the DV was hypothetical self-isolation, and the IVs were the round number, the number of infections, the self-isolation of others in the previous round, and others’ self-isolation in the scenario. The model also included participants’ IDs as the random intercept and the round number as the random slope.

A Wilcoxon Signed Rank (WSR) test was used to measure the difference between hypothetical self-isolation and incentivised self-isolation (H4). Here we averaged self-isolation for each category (i.e., hypothetical or incentivised trials) per participant, such that each participant had one observation in each category. Only the hypothetical scenario was used that the participant believed would happen (e.g., when the participant indicated they believed others would choose moderate self-isolation levels, then that hypothetical self-isolation response would be used for this analysis). To measure the effect of the cost of lockdown on incentivised self-isolation (H5), we also used a WSR test. The WSR test was used in these instances because the tests are designed to only detect a main effect, disregarding any interactions.

Analyses were conducted using R32, mainly relying on the “afex” package33 and the “emmeans” package34. Results were considered significant based on a false discovery rate adjusted α of 0.05.

Exploratory analysis

One exploratory analysis was conducted to investigate whether participants consistently self-isolated more than they believed others would. This analysis consisted of a WSR, testing the difference between incentivised self-isolation (aggregated per player) and beliefs about others’ behaviour (aggregated per player).

The preregistration can be found here https://osf.io/xhf7w/?view_only=c3f6f12d380d414f8584e19b7a934294; the data, analysis code, and code for the experimental software are all publicly available on the Open Science Foundation website here https://osf.io/jcmwt/?view_only=d7b6fe0e5e53447ca871312b2b10f779.

Ethical approval

This research was approved by the Monash University Human Research Ethics Committee (Project ID: 26499). The experiment was performed in accordance with relevant named guidelines and regulations. Informed consent was obtained from all participants and/or their legal guardians.

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