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Analysis of player decisions in a mobile game to study the influence of wealth on risk aversion
Last registered on May 13, 2020

Pre-Trial

Trial Information
General Information
Title
Analysis of player decisions in a mobile game to study the influence of wealth on risk aversion
RCT ID
AEARCTR-0005847
Initial registration date
May 13, 2020
Last updated
May 13, 2020 3:37 PM EDT
Location(s)

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Primary Investigator
Affiliation
LMU Munich
Other Primary Investigator(s)
PI Affiliation
Leibniz University of Hannover
PI Affiliation
LMU Munich
PI Affiliation
LMU Munich
Additional Trial Information
Status
In development
Start date
2020-05-16
End date
2020-07-15
Secondary IDs
Abstract
We analyze the choices available to players of a mobile game, which is a closed economic system. The players’ decisions under risk allow us to estimate changes of risk aversion when wealth changes. In contrast to previous literature, we are able to exclude inertia and the asset integration problem. The field experiment allows for tests against the null hypothesis of constant absolute risk aversion and constant relative risk aversion.
External Link(s)
Registration Citation
Citation
Huber, Tobias et al. 2020. "Analysis of player decisions in a mobile game to study the influence of wealth on risk aversion." AEA RCT Registry. May 13. https://doi.org/10.1257/rct.5847-1.0.
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Experimental Details
Interventions
Intervention(s)
This is a measurement study and the choice problems will occur randomly. We randomly split the subjects into Group G1 and Group G2. The group designation determines which choice problems the subjects face (see below).
Intervention Start Date
2020-05-16
Intervention End Date
2020-07-15
Primary Outcomes
Primary Outcomes (end points)
At different levels of in-game wealth w, the subjects choose between taking part in a lottery or receiving a safe payment (see below). We examine how the probability to choose the safe payment depends on the in-game wealth level w. Thus, we can deduct how the Arrow-Pratt coefficient of absolute risk aversion and the Arrow-Pratt coefficient of relative risk aversion depend on the in-game wealth level w.
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).
Secondary Outcomes
Secondary Outcomes (end points)
Secondary Outcomes (explanation)
Experimental Design
Experimental Design
This study is a measurement study and the choice problems will occur randomly. We randomly split the sample into two groups. The group designation determines which choice problems the subjects face (see above).
Experimental Design Details
Not available
Randomization Method
Subjects are randomly allocated to the two groups when agreeing to the consent form.The specific lottery displayed after every successful completion of the game is chosen randomly by the computer.
Randomization Unit
The randomization unit of the group allocation is the individual player. Specific choices from the group menu are randomly allocated after every successful game completion.
Was the treatment clustered?
No
Experiment Characteristics
Sample size: planned number of clusters
Not applicable to our case (see above).
Sample size: planned number of observations
Our setting deviates from traditional experiments in the sense that the number of downloads in Google’s Play Store determines the number of subjects in our experiment. We will upload the game to Google’s Play Store on 8 May 2020 and expect the game to be public at latest after 7 days (depending on Google’s Play Store). We will additionally upload a promotional video to YouTube on 16 May 2020 (this date is, however, subject to discretion of the promoting influences). We expect only a small number of game downloads until the release of the promotional video and thus see the date of the promotional video as our trial start. 60 days after the release of the promotional video we stop collecting data. The sample size of our experiment is therefore dependent on the number of downloads from Google’s Play Store and the game’s retention rate. Thus, the sample size is not predictable at this stage. We will additionally filter our data as described below and provide for each filter the corresponding reason in parentheses: (1) We remove players that are uniquely identifiable based on the collected demographic variables (self-reported age, self-reported gender, and country). [data protection law] (2) We are only allowed to process the choice of players that specify an age greater or equal to 16. [data protection law] (3) Both lotteries L_A and L_R will show up not before a total in-game wealth level of at least 100. [experimental design] (4) Both lotteries L_A and L_R will only show up if a player reaches at least 10 points in the corresponding run. [experimental design]. (5) The first three decisions of our subjects may be systematically different than the subsequent decisions because subjects examine in the first rounds how the game and how the lotteries work. Therefore, we plan to conduct two analyses: (a) We include all decisions of our subjects. (b) We exclude the first three decisions of our subjects. [learning behavior]
Sample size (or number of clusters) by treatment arms
We have two treatment arms. In each treatment arm, we have half of the total number of subjects.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
In the aggregated analysis, a power test is not applicable to our case. The sample size is dependent on the number of downloads from Google’s Play Store and the game’s retention rate and is, thus, not predictable at this stage. In the individual analysis, we only consider subjects that have made at least 150 decisions. The power test underlying this value assumes that subjects with the smallest amount of wealth (100) are indifferent at the third lowest certain payment, while subjects with a wealth higher than the prize of the highest in-game reward (5100) are indifferent at the tenth lowest certain payment. Subjects decide according to a stochastic decision model with contextual utility functions and a logistic error term using an inverse error parameter of 15. Under these assumptions and a statistical significance level of 5%, subjects with 150 decisions will be detected to have a non-zero coefficient of wealth on risk aversion 50% of the time.
Supporting Documents and Materials

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IRB
INSTITUTIONAL REVIEW BOARDS (IRBs)
IRB Name
See the attached document "Comment_IRB_Approval"
IRB Approval Date
2017-11-22
IRB Approval Number
N/A