Causal Evidence on Illusion of Control in a Complex Environment

Last registered on April 14, 2024

Pre-Trial

Trial Information

General Information

Title
Causal Evidence on Illusion of Control in a Complex Environment
RCT ID
AEARCTR-0008469
Initial registration date
October 30, 2021

Initial registration date is when the trial was registered.

It corresponds to when the registration was submitted to the Registry to be reviewed for publication.

First published
November 01, 2021, 12:54 PM EDT

First published corresponds to when the trial was first made public on the Registry after being reviewed.

Last updated
April 14, 2024, 3:35 AM EDT

Last updated is the most recent time when changes to the trial's registration were published.

Locations

Region

Primary Investigator

Affiliation
University of Bonn

Other Primary Investigator(s)

Additional Trial Information

Status
Completed
Start date
2021-11-03
End date
2022-01-31
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Abstract
I study the effect of how players in a board game generate their rolls on subjects' beliefs of certain players' winning probabilities in a board game. In particular, it is varied whether players use a tablet computer vs. whether they use a physical die and a dice shuffler to generate their die rolls. The study is implemented as an RCT laboratory experiment.

See also the attached pre-analysis plan.
External Link(s)

Registration Citation

Citation
Laubel, Alexander. 2024. "Causal Evidence on Illusion of Control in a Complex Environment." AEA RCT Registry. April 14. https://doi.org/10.1257/rct.8469-2.0
Experimental Details

Interventions

Intervention(s)
Laboratory experiments to study the effect of whether a die roll is generated by a computer vs. by physically rolling a die on beliefs of winning probabilities in a board game.

For more details, see attached pre-analysis plan.
Intervention (Hidden)
Intervention Start Date
2021-11-03
Intervention End Date
2022-01-31

Primary Outcomes

Primary Outcomes (end points)
'Belief1,' 'Belief2,' 'Belief3:' Subjects' beliefs (incentivized) of the probability that a certain player wins a board game given a specific game situation. These three beliefs are elicited over the course of a match of a board game. The probability elicited over is the respective winning probability at the specific game situation when the elicitation takes place.

For more details, see the attached pre-analysis plan.
Primary Outcomes (explanation)

Secondary Outcomes

Secondary Outcomes (end points)
'BeliefBackward:': after the match subjects are asked to reassess Belief1 again.

'BeliefCounterfactual:' after the match subjects are asked to reassess Belief1, hypothesizing to be in the other treatment condition.

For more details, see the attached pre-analysis plan.
Secondary Outcomes (explanation)

Experimental Design

Experimental Design
See also the attached pre-analysis plan.


I. DATA COLLECTION

In the BonnEconLab at the University of Bonn, I will conduct laboratory experiments. The basic structure of the experimental setup is as follows. Each session corresponds to one match of a board game Ludo and consists of 3 subjects. Two subjects have the roles of players in the boardgame Ludo in a two-players version as an actual, physical board game. For clarity, let me call these subjects ‘player 1’ and ‘player 2,’ respectively. Additionally, the third subject observes the course of the game as it is played by subjects in the player roles. For clarity, let me call this subject observing the match ‘observer.’

Over the course of a session (i.e., one match) each subject is asked multiple times to estimate the probability that a certain player wins given the current state of the game. Each subject in the player role is asked to estimate the winning probability of they themselves winning given the current state of the game. The subject in the observer role is asked to estimate the winning probability of one specific player (‘player 1’) given the current state of the game.

Treatment allocation is between-sessions. There are two treatment conditions: Control and Treated. The treatment conditions concern how subjects in the player roles generate their die rolls during the boardgame. In Control, both players generate their die rolls with a ‘die roll computer’ each. This ‘die roll computer’ is a tablet computer that displays an image of a die roll realization upon clicking a button. In Treated, player 2 generates his die roll with a die roll computer in exactly the same manner as in Control, but crucially player 1 now uses a physical die and a dice shuffler to generate the die rolls.

The board and the realizations of the die rolls (both if they are generated by the computer and if they are generated by physical die rolls) are livestreamed to the subject in the observer role and to the experimenter in order to monitor that, e.g., players do not cheat. The subject in the observer role and the experimenter are both placed in separate rooms than the subjects in the player roles, who are also placed in separate rooms.

Over the course of the game, subjects provide three incentivized beliefs Belief1, Belief2 and Belief3. Regarding incentivization, one of these three beliefs is randomly selected on the subject level, and incentivized via a binarized-scoring rule.

Due to COVID-19 restrictions, each subject – including the subjects in the roles of player 1 and player 2, respectively – is seated in an individual room. Between the two rooms of the subjects in the player roles, there is an open door frame, in which a table with the board game is positioned.

In more detail, the experiment consists of the following stages:

Pre-game:
• Subjects enter the laboratory and are allocated to separate rooms.
• In each room, there is a computer. This computer is used to display on-screen instructions to subjects, and subjects also enter all data that is collected via this computer. Additionally, in each room the rules of the game Ludo are provided in a printed-out version. Subjects in the observer role have an additional monitor that is used to display the livestream of the game as it is played by subjects in the player role.
• Additionally, in the door frame between the rooms of players 1 and 2 there is a table with a ludo board and the means used to generate the die rolls (i.e., depending on the treatment condition, a tablet computer and a physical die with a dice shuffler, or two tablet computers)
• After subjects have read the instructions, they answer comprehension questions (see VI. EXCLUSION CRITERIA below).

During the game:
• The board game does not start from the beginning, but has as its initial situation an end-game situation where the entire remainder of the game is pinned down by the die roll realizations. In other words, the remainder of the game is such that subjects only execute the die roll realization without making decisions that impact the course of the game.
• Before players make the first move, all three subjects are asked to evaluate winning probabilities in the following way: player 1 and the observer are asked to evaluate player 1’s winning probability, and player 2 is asked to evaluate player 2’s winning probability. These beliefs of the winning probabilities are referred to as ‘Belief1’.
• Afterwards, the game is played, while die rolls are generated according to the treatment condition until both players have taken two turns.
• After both players have taken two turns, subjects again enter their beliefs of the winning probabilities of the same players as for Belief1: player 1 and the observer are asked to evaluate player 1’s winning probability, and player 2 is asked to evaluate player 2’s winning probability. These beliefs are referred to as ‘Belief2.’
• Afterwards, the game is resumed until one player can win the game with the next die roll.
• When this is the case, subjects again enter their beliefs of the winning probabilities of the same players as already for Belief1 and Belief2: player 1 and the observer are asked to evaluate player 1’s winning probability, player 2 is asked to evaluate player 2’s winning probability. These beliefs are referred to as ‘Belief3.’
• Afterwards, the players finish the game.

Post-game:
• Post-game data is elicited (in the following order): BeliefBackward, a questionnaire block (demographic and psychological), BeliefCounterfactual
o BeliefBackward: subjects are asked to reassess the initial end-game situation (when they entered Belief1) assuming that the game is played again (with new die roll realizations) from this same initial end-game situation, and assuming die rolls to be generated in the same way as before (i.e., they should assume to be in the same treatment condition). Subjects are provided a photo of the initial situation. This belief elicitation is unincentivized.
o Demographic questionnaire eliciting data on: Age, Gender, Occupation, Education, Study Field, Political Orientation, Income, Household Form, Religiosity, Number of Siblings, Number of Children.
o Psychological questionnaire:
 Eliciting data on: Locus of Control, Beliefs on Sources of Social Inequality, Self Esteem.
 All of these concepts are elicited using Likert-scale questions as suggested and used by the German Socio-Economic Panel (SOEP).
 Also following the SOEP survey manual, the questions on Beliefs about Sources of Social Inequality (that inquired upon the degree to which subjects believe certain factors to be de facto sources of social inequality) are further distinguished into those addressing ‘illegitimate means’ (e.g., inheriting wealth) and those addressing ‘legitimate means’ (e.g., exerting a lot of effort). In my data analysis (see below), I will construct separate scalar indices for illegitimate and legitimate means.

o BeliefCounterfactual: subjects are asked to reassess the initial end-game situation (when they entered Belief1) assuming that the game is played again (with new die roll realizations) from this same initial end-game situation and assuming that die rolls are generated as they had been in the other treatment condition. That is, in a Treated session all three subjects are asked to imagine that both player 1 and player 2 use a tablet computer each to generate their die rolls. Likewise, in a Control session all three subjects are asked to imagine that player 1 now uses a physical die and a dice shuffler, while player 2 continues to use the tablet computer to generate the die rolls. Subjects are provided a photo of the initial situation. This belief elicitation is unincentivized.


II. TREATMENTS

Treatment allocation happens between-sessions, i.e., all subjects in one session have the same treatment condition.

1. Treatment Treated
Player 1 uses a physical die and a dice shuffler to generate her die rolls. Player 2 uses a die roll computer (i.e., a tablet that displays a die roll realization upon clicking a button).



2. Treatment Control
Both player 1 and player 2 use a die roll computer each (i.e., a tablet that displays a die roll realization upon clicking a button).

All subjects are explicitly told how both players generate their die rolls during the on-screen instructions. Additionally, the observer is reminded of this information during the belief elicitation.

Everything else is held equal between sessions. In particular, all sessions start from the same initial end-game situation.

Moreover, each session in Control is matched to a session in Treated in the following way: in order to reduce noise and to increase statistical power (in particular regarding the analysis involving Belief2 and Belief3 – see below), after a Treated session is run, a corresponding Control session is run with exactly the same die realizations. That is, while in Treated sessions, subjects actually generate the die rolls with a physical die (player 1) or the die roll computer (player 2), in Control the two die roll computers do not actually generate the die rolls, but only display die rolls of a previous Treated session that were randomly generated back then. Every Control session corresponds to exactly one Treated session in this manner.
Experimental Design Details
Randomization Method
Randomization done in office by a computer
Randomization Unit
Session
Was the treatment clustered?
Yes

Experiment Characteristics

Sample size: planned number of clusters
110 sessions
Sample size: planned number of observations
330 subjects in the laboratory.
Sample size (or number of clusters) by treatment arms
55 session "Control", 55 sessions "Treated".
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
IRB

Institutional Review Boards (IRBs)

IRB Name
IRB Approval Date
IRB Approval Number
Analysis Plan

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Post-Trial

Post Trial Information

Study Withdrawal

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Intervention

Is the intervention completed?
Yes
Intervention Completion Date
January 31, 2022, 12:00 +00:00
Data Collection Complete
Yes
Data Collection Completion Date
January 31, 2022, 12:00 +00:00
Final Sample Size: Number of Clusters (Unit of Randomization)
110 sessions (with 3 subjects each).
Was attrition correlated with treatment status?
No
Final Sample Size: Total Number of Observations
330 subjects.
Final Sample Size (or Number of Clusters) by Treatment Arms
110 subjects per treatment arm (one subject of each treatment arm per session).
Data Publication

Data Publication

Is public data available?
No

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Program Files

Program Files
No
Reports, Papers & Other Materials

Relevant Paper(s)

Reports & Other Materials