Basic demographic information collected from the participants in the study is shown in Table S1
. The distribution of participants is very similar across the two conditions, indicating successful random assignment by our game program. To control for individual characteristics which may affect the decision to self-protect, our empirical analysis of players' behavior later on makes use of these demographic data.
Prevalence—the fraction of infected players—as well as the percentage of healthy players using the safe action—which we refer to as the rate of safe behavior—in every round for each of the conditions are shown in . An epidemic phase is observed initially—up to rounds 9 or 10. Thereafter, the virtual disease appears to enter into an endemic phase. To avoid issues with multicollinearity, our empirical analysis later on utilizes only observations from round 10 onwards. Therefore, our results can be interpreted as how people behave when a disease is endemic, rather than during the initial stage. As can be seen from , a significant proportion of healthy players engaged in self-protective behavior during the course of the game; consequently, the prevalence of the virtual disease was substantially lower than the level that would obtain if no one ever chose the safe action.
Prevalence of disease and rate of safe behavior in the game.
To get a sense of how often players were infected, we examined the distribution of players according to the number of times they acquired an infection. The results (see Figure S3
) show that the proportion of players who were infected a high number of times (at least three) is greater in the high cost condition, while the low cost condition yielded a higher fraction of players who were infected two or fewer times.
Because choosing the safe action in our game involves actively clicking on a button on the computer screen, while the risky action can be chosen by clicking on the appropriate button or by not clicking on any buttons (recall that the risky action is the default option if a healthy player does not submit an action choice by the end of any round), we also examined the rate with which the players actively entered a choice when they were healthy—which we refer to as the choice rate
here. The results are given in Table S2
. The distribution of choice rates is bimodal in the two conditions, with most of the players having an extremely high or extremely low choice rate. About half of the participants had a choice rate of at least 80%, and 63% of all the players had a choice rate greater than 60%. We note that while 34% of the players had a choice rate of less than 20%, 86% of all the players completed the end-of-study questionnaire. This suggests that some of the players with a low choice rate were in fact attentive to the game and intentionally let the computer select the default option for them during the game. In what follows—unless noted otherwise—we will describe a player as having chosen the risky action whether the player actively entered a choice of the risky action or let the computer pick it as the default option.
We hypothesized that the prevalence of disease in the previous round would affect the propensity a player has for engaging in self-protective behavior. Specifically, the likelihood that a player will choose the safe action should be increasing in the previous-round prevalence since the chances of acquiring an infection from engaging in risky behavior (and, hence, of earning fewer points in the game) are higher when more people are infected. Such prevalence-dependent behavior is predicted by many theoretical models in economic epidemiology, such as those presented in 
. As shown in , in the high- and low-cost conditions, the fraction of healthy players choosing the safe action in any round rises when the prevalence in the previous round increases. Moreover, the effect of prevalence on behavior is stronger when the cost of the safe action is low. In other words, players' behavior is more sensitive to prevalence when it is cheaper for them to adopt the self-protective action.
The relationship between prevalence and rate of safe behavior in the following round.
Interestingly, for either the high- or low-cost condition, the relationship between players' behavior and disease prevalence seems to depend on how many rounds—i.e., how much time—have elapsed in the game. As can be seen from , in either condition, players' behavior appears to be more sensitive to a prevalence change in the latter rounds compared to the early-to-middle part of the game.
Relationship between prevalence and rate of safe behavior—the effect of the number of rounds elapsed.
A player's risk preferences should affect the player's behavior in the game since the choice between the safe action and the risky action is also a choice between a “sure thing” and a gamble that can yield—relative to the sure thing—either a higher or a lower payoff. Thus, all else being fixed, we would expect the likelihood of choosing the safe action to be higher for someone who dislikes risk immensely compared to someone who is not as averse to risk. Although there is no direct way to measure a player's risk preferences in our study, it is reasonable to assume that players who chose the safe action the first time they had a chance to make a decision are more risk-averse than those who chose the risky option for their first action. (Note that, except for the three players in each condition that were randomly selected to be infected in round 1, a player's first choice of action is the action choice in round 1.) Because a player's first action choice is not a function of the player's experience or history with the virtual epidemic, it should be determined to a large extent by a player's risk preference. shows the comparison between the rate of safe behavior among those who chose the safe action as their first action and the rate of safe behavior among those players whose first action is the risky action. For both conditions, the rate of safe behavior among players who chose the safe action as their first action is higher in every round of the game than the rate of safe behavior among the players who chose the risky action first. When we omit from consideration players who never chose the safe action, and compare the rate of safe behavior of those whose first action was the safe action to the rate of safe behavior among those players who chose the safe action at least once and whose first action was the risky one, we obtain a similar result: except for rounds 39 through 44 in the low cost condition, the rate of safe behavior is higher among the players who chose the safe action for their first action (see Figure S4
). These results are consistent with the hypothesis that players who are more averse to risk—and thus more likely to choose the safe action for their first choice—engage in self-protective behavior at a higher rate throughout the virtual epidemic.
Comparing the rate of safe behavior among those whose first action was the risky action to the rate of safe behavior among those whose first action was the safe action.
To get a better sense of what determines the players' choice of actions in the game when they are healthy, we performed a probit analysis with the probability of choosing the safe action as the dependent variable (we obtained similar results using a logit analysis; see Table S5
). We included as independent variables the cost of the safe action, the prevalence of disease in the previous round, and players' first action choice to account for individuals' attitude towards risk. Furthermore, we incorporated the demographic information collected from the end-of-study questionnaire since personal attributes such as gender may affect the propensity a player has for engaging in self-protective behavior.
Because a player's decision in any round may be affected by the player's experiences from taking the risky action from earlier in the game, we also added a measure of how often the player was infected in previous rounds—adjusting for how many times the player chose the risky action in the past—in our empirical model. We refer to this measure by infectriskratio, defined to be the number of times a player has been infected divided by the number of times a player's action was the risky one. Given the results shown in —specifically, the finding that players' behavior appears to be more sensitive to prevalence later in the game—we included the number of rounds elapsed and a prevalence-round interaction term in the empirical analysis to determine whether having more experience with the virtual epidemic affects the way players respond to the news update on disease prevalence.
Our empirical model is given as follows:
1 if the i
-th individual chooses to self-protect in round r
, and 0 otherwise. Xi
is a vector of demographic characteristics including gender, race, education, marital status, and employment status. Table S4
gives the definitions of the terms in (2). Assuming the error term is normally distributed, we can use a standard probit model to estimate the coefficients in equation (2)
. As mentioned previously, because prevalence is highly correlated with rounds early in the game—up to round 10—we restricted our data sample to observations from round 10 and beyond.
Marginal effects derived from the probit results are given in . All players are included in the empirical model in the first two columns, while columns (3) and (4) show the results when restricting the sample to only those players with a choice rate of over 60%. The difference between the first and second columns—and between the last two columns—lies in how the dependent
variable is defined. In columns (1) and (3), a risky action is considered to be any response other than the safe action—thus, either clicking on the button for the risky action or letting the computer select the default option is counted as a risky action. On the other hand, in columns (2) and (4), only clicking on the button for the risky action is considered to be taking the risky action—not clicking on a button and letting the computer pick the default option is counted as a missing response in the probit analysis. (In defining the independent variables infectriskratio
, any response other than the safe action is counted as a risky action.) For brevity, we omitted the results for the demographic variables from since, for the most part, the players' behavior does not depend on them (see Table S3
). In particular, we note that while some studies of risk-taking behavior have found that women in general are more risk-averse than men 
, we did not find evidence of this in our study as the gender coefficient in our probit analysis is not statistically significant.
Table 1 Marginal effects evaluated at the mean using probit results of estimation of equation (2).
Except for the first model (column 1)—in which the coefficient on cost is not significant—the probit results show that the likelihood of choosing the safe action is higher when its cost is lower. Specifically, all else equal, players in the low cost treatment are roughly 20 percentage points more likely to choose the safe action than players in the high cost treatment. This indicates that the cost of preventative measures plays a critical role in individuals' decision to engage in self-protection.
Our probit analysis also shows that the players do respond to information regarding disease prevalence—and that their responsiveness to prevalence increases over time. The marginal effects shown in indicate that the impact of the reported prevalence on the probability of picking the safe action is strictly increasing by round (from (2), the size of this effect is given by β2+β6
round). For instance, all else being the same, a 10 percentage point increase in the reported prevalence in round 10 would on average lead to a 4-to-5 percentage point increase in the probability of selecting the safe action. This impact increases to between 9 and 11 percentage points by round 20, and 22 to 23 percentage points by the end of the game.
The variable firstaction is statistically significant in all the specifications that we examined, which tells us that players' risk preferences do play a role in how likely they are to engage in self-protective behavior. Specifically, players that revealed themselves to be more risk-averse by choosing the safe action at their first opportunity are roughly 20 percentage points more likely than their less risk-averse peers to choose the safe action in any round, all else equal. This effect is significantly bigger in column (1), at 38 percentage points, but once we focus on players with a high choice rate (at least 60%), we find a fairly robust impact. This indicates that the first result is likely picking up the fact that more risk-averse players are also more likely to have a high choice rate.
Our results show that players' behavior in the virtual epidemic is highly dependent on how many rounds have elapsed in the game and on the outcomes of their (risky) actions in earlier rounds. The coefficient on infectriskratio
is positive and significant, indicating that players who were infected more often earlier in the game—adjusting for the number of times they chose the risky action—are more likely to self-protect in later rounds. For example, if a player's history increased from getting infected only once per 4 risky actions (infectriskratio
0.25) to being infected once for every 2 risky actions (infectriskratio
0.5), the player's probability of choosing the safe action would increase by 12.5 percentage points, all else being equal. Therefore, holding prevalence constant, one's history with the disease has a significant impact on self-protection behavior; the worse the experiences one has had with the disease, the more likely the player is to self-protect in the future.
How the number of rounds that have taken place since the start of the epidemic affects players' behavior depends on the disease prevalence. From (2), this effect can be measured by β5+β6
prevknown. Holding all else constant, if the prevalence is high, say, around 0.4 (and remains fixed), then the likelihood that a player would choose to self-protect increases over time. For instance, from the specification shown in column 1 of , the probability of selecting the safe action rises by 3.7 percentage points for every 10 rounds that go by. Similar results obtain using the other specifications shown in . This tendency for players to become more “cautious” as the epidemic progresses is even stronger when the prevalence is higher. Assuming that prevalence is fixed at 0.5, for example, the probability of choosing the safe action increases by 9 percentage points for every 10 rounds.
The opposite, however, is true when prevalence is low, i.e., when the number of infected individuals is small, players are less likely to self-protect over time. For a prevalence level of 0.2, the probability of picking the safe action falls between 6 and 10 percentage points every 10 rounds, depending on which specification we look at. The decline is even steeper—between 12 and 16 percentage points—when the prevalence is 0.1. This result suggests that while an epidemic may originally have a strong impact on behavior, the overall salience of the disease may diminish over time when prevalence is low, thus leading to a decrease in self-protection. Such an effect is reminiscent of condom fatigue—the declining use of condom as a preventive measure—in the context of HIV/AIDS prevention.