Non-Linear Public Goods Games
Last registered on July 06, 2021


Trial Information
General Information
Non-Linear Public Goods Games
Initial registration date
May 28, 2021
Last updated
July 06, 2021 4:27 PM EDT
Primary Investigator
University of Potsdam
Other Primary Investigator(s)
Additional Trial Information
Start date
End date
Secondary IDs
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
Andres, Maximilian. 2021. "Non-Linear Public Goods Games." AEA RCT Registry. July 06.
Sponsors & Partners
Experimental Details
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
Intervention End Date
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.

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.

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.
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?
Experiment Characteristics
Sample size: planned number of clusters
I plan to ran 7 sessions per treatment with a minimum of 12 subjects to achieve a power of 0.9.
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)
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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