Non-Linear Public Goods Games

Last registered on October 01, 2021

Pre-Trial

Trial Information

General Information

Title
Non-Linear Public Goods Games
RCT ID
AEARCTR-0007741
Initial registration date
May 28, 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
May 28, 2021, 12:50 PM EDT

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

Last updated
October 01, 2021, 12:40 PM EDT

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

Locations

Region

Primary Investigator

Affiliation
University of Potsdam

Other Primary Investigator(s)

Additional Trial Information

Status
Completed
Start date
2021-06-07
End date
2021-06-18
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Abstract
I present a theory on non-linear Public Goods. The Game has a continuum of Nash equilibria in the interior of strategy space which depend on the degree of curvature and what players belief others will contribute. I will use laboratory experiments to test the theory: average contributions in non-linear Games are higher than in quasi-linear Games.
External Link(s)

Registration Citation

Citation
Andres, Maximilian. 2021. "Non-Linear Public Goods Games." AEA RCT Registry. October 01. https://doi.org/10.1257/rct.7741
Sponsors & Partners

Sponsors

Experimental Details

Interventions

Intervention(s)
I use a between-subject design to study how diffraction between the Public Good and contribution affects investments in the Public Goods Game. To this aim, I conduct two treatments in the lab: Non-Linear (h = 0.5) and Quasi-Linear (h = 0.99).
Intervention Start Date
2021-06-07
Intervention End Date
2021-06-18

Primary Outcomes

Primary Outcomes (end points)
- group contributions M (sum of contributions per group)
- individual contributions m (average of contributions per group)
Primary Outcomes (explanation)
If the predictions about the implication of the diffraction parameter h on contributions to the Public Good hold I should observe group investments M which are, on average, higher in Non-Linear than in Quasi-Linear. I compute sample sizes for a comparison which I want to include but yield a high number of subjects: M per round, for example, the last round such that subjects have time to understand the game.

Secondary Outcomes

Secondary Outcomes (end points)
- individual beliefs b
Secondary Outcomes (explanation)
When the belief b of the sum of others' contribution are correct, individual contributions m should top up other's contributions to the Public Good.

Experimental Design

Experimental Design
Public Goods Game:
Similar to much of the literature, in each of the r=10 rounds each of the n=4 subjects receives an endowment of z=20 points. Thus, Z=80. The decision about how much to contribute to the Public Good in each round m is made simultaneously. The Public Good is multiplied by b=2 and then evenly distributed among all group members. Following each round, subjects receive feedback about their own contribution, the sum of contribution of other's in their group and their own payoff in that round.

I inform subjects about the function G() to ensure that it is common knowledge. To this aim, I explain the formula of the Public Goods Game to subjects and inform them about their payoff from the Public Good given any allocation in the Public Good. In addition, I provide a direct response tool to ensure that subjects understand the structure of the game. Further, I use a quiz to ensure that subjects gain an understanding of the game. I apply an exchange rate between points and euro which ensures that subjects had an incentive to increase their earnings. The subject's final earnings were proportional to their earnings in points, plus a show-up fee.

Treatments:
I use a between-subject design to study how diffraction between the Public Good and contribution affects investments in the Public Goods Game. To this aim, I conduct two treatments in the lab: Non-Linear (h = 0.5) and Quasi-Linear (h = 0.99). I will use results to test the hypothesis: average group contributions in non-linear Games are higher than in quasi-linear Games.

Questionnaire:
As shown in the theory, in the non-linear Public Goods Game, the Nash equilibrium includes what players belief others will contribute. Thus, to elicit beliefs is of some interest. To prevent any contamination of behavior in the Public Goods Game, I elicit beliefs in the tenth round immediately after subjects chose their contribution. I incentives subject's for correct beliefs, but it was small, to avoid hedging.
Experimental Design Details
I note that a sufficient technical setup is essential not only for using the direct response tool but also for reading instructions and taking part during the session. Participants who registered for the experiment agree that they have a sufficient technical set up; for example, a sufficient internet connection, computer and browser.

However, it turned out during a session that this is not always the case. I will deal with this issue in the following way: If I note participants lack a sufficient technical set up during the welcoming, we will not let them take part. If I note in conversations (i.e. chat messages and breakout rooms) during the experiment (i.e. during the instruction and contribution procedure) that a participant does not have a sufficient technical set up to use the direct response tool, read instructions or contributing during the session, I will exclude the corresponding session from my analysis. I will apply this exclusion criterion to a past session (June 7, 2021, 2pm) where I noted during the experiment that three participants were lacking a technical set up to use the direct response tool properly and read instructions because of an insufficient technical set up, and disregarded the rules. I have not looked at the data of the respective session.
Randomization Method
Students were recruited randomly via electronic mail that were send to their student mail account.
Randomization Unit
Group level randomization for both Non-Linear (h = 0.5) and Quasi-Linear (h = 0.99).
Was the treatment clustered?
No

Experiment Characteristics

Sample size: planned number of clusters
I plan to ran 7 sessions per treatment with a minimum of 12 subjects.
Sample size: planned number of observations
In total, 168 subjects.
Sample size (or number of clusters) by treatment arms
84 subject in Non-Linear and 84 Subjects in Quasi-Linear
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
I changed from a partner- to a stranger-matching protocol shortly before the experiment, but did not changed the power calculation because the theory predicts actual values. However, in order to be as transparent as possible, I present the power calculation in the following. One-sided Wilcoxon-Mann-Whitney-Test, alpha = 0.05, Power = 0.9 and allocation ratio of 1 yields a sample size (a group) per treatment of 19 (assumptions: mean group Non-Linear equals 5, SD = 2; mean group Quasi-Linear equals 3, SD = 2).
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IRB

Institutional Review Boards (IRBs)

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IRB Approval Date
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Post-Trial

Post Trial Information

Study Withdrawal

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Intervention

Is the intervention completed?
Yes
Intervention Completion Date
June 11, 2021, 12:00 +00:00
Data Collection Complete
Data Publication

Data Publication

Is public data available?
No

Program Files

Program Files
Reports, Papers & Other Materials

Relevant Paper(s)

Reports & Other Materials