Primary Outcomes (explanation)
We present subjects in Group G1 the fixed lottery L_A = (150, 0.5; 10, 0.5) and vary the safe payment c_A between 60 and 90. Furthermore, we present participants in Group G2 the lottery L_R = (0.15w, 0.5; 0.01w, 0.5) and vary the safe payment c_R between 0.06w and 0.09w. We use decisions of Group 1 to examine how the coefficient of absolute risk aversion depends on in-game wealth and decisions of Group 2 to examine how the coefficient of relative risk aversion depends on in-game wealth. For Group 1 (Group 2), we can reject constant absolute (relative) risk aversion in wealth if we observe that people make systematically different choices at different wealth levels w.
Analysis A1 is descriptive. We plot the relative frequency of safe decisions in dependence of in-game wealth and our demographic variables (self-reported age, self-reported gender, country). For this, we bin in-game wealth levels in steps of 100, self-reported age in steps of 10, and distinguish between Germany and non-Germany.
Analysis A2 is inductive. We run a linear regression with the probability of a safe choice as dependent variable and the in-game wealth level as independent variable. The model additionally includes controls (self-reported age, self-reported gender, country) and their
interactions with the in-game wealth. The analysis also includes fixed effects for the different lotteries offered to the subjects. We will estimate one model including only control variables and one model which also includes subject fixed effects. Standard errors are heteroscedasticity-robust and clustered on the level of the subject.
Analysis A3 is inductive. We estimate a structural model in which wealth and control variables determine the risk aversion coefficient directly. The estimation is basically a Probit estimator with the risk aversion coefficient of the subjects as the underlying variable. The model’s outcome is the probability that this coefficient is higher or lower than the risk aversion coefficient implied by indifference in the lottery that the subjects face. The risk aversion coefficient is modeled as a linear function of the control variables and can be dependent on the wealth level in a linear or quadratic fashion, the three demographic control variables (self-reported age, self-reported gender, country) will further be interacted with wealth. Standard errors are clustered on the level of the subject.Moreover, both Analysis A2 and A3 include an indicator, which equals one if the upper outcome of the lottery (but not the safe payment) enables to purchase a new skin in the game’s shop if added to the current in-game wealth level. This aims to control for systematically different choices at levels of wealth that are close to the price of a skin. We additionally collect a variety of in-game data, which are potential interesting control
variables for inductive multivariate tests. However, we will not interact them with the in-game wealth because this does not address our main research question.
We will also perform Analysis A2 and Analysis A3 on an individual level and report the share of significant positive/negative coefficients and the share of insignificant coefficients based on all considered individuals. In the individual analysis, we only consider subjects that have made at least 150 decisions. This number of decisions is supported by a power test (see below).