Public goods games under a nonlinear tax system with an interior dominant strategy equilibrium
Last registered on January 18, 2019


Trial Information
General Information
Public goods games under a nonlinear tax system with an interior dominant strategy equilibrium
Initial registration date
June 13, 2018
Last updated
January 18, 2019 5:37 PM EST

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Primary Investigator
University of California, Irvine
Other Primary Investigator(s)
Additional Trial Information
In development
Start date
End date
Secondary IDs
In the standard Voluntary Contribution Mechanism (Hichri 2004), a linear public goods game, the dominant strategy equilibrium is to donate zero; therefore, any error or noise will appear to be altruism. I avoid this ``corner critique'' (Laury and Holt 2008) by using a nonlinear tax system to get an interior Nash equilibrium. It is also possible to do this by means of a threshold for the good to be provided; however, this induces a multiplicity of equilibria. My method induces a unique, sharp dominant strategy equilibrium, in which a player's best response does not depend on any other players' choices. Furthermore, by using a differentiable payoff function, I can measure the marginal cost of deviation from the dominant strategy equilibrium, inferring a willingness-to-pay for other-regarding behavior. Using software that provides real-time feedback about payoffs, I will test whether participants contribute more than the dominant strategy equilibrium, under treatments that vary the payoffs and the inequality of endowments such that both the equilibrium and the Pareto optimum are different across each treatment condition.
External Link(s)
Registration Citation
Julius, Patrick. 2019. "Public goods games under a nonlinear tax system with an interior dominant strategy equilibrium." AEA RCT Registry. January 18.
Experimental Details
Participants will be randomly assigned to groups, given endowments, and offered the chance to make contributions to their groups. Contributing to the group will benefit all members of the group, but at a cost to the individual making the contribution. Whatever remains of the endowment not contributed will then be "taxed" according to a rule that generates an interior dominant strategy equilibrium.

Interventions will vary the costs and benefits of "tax" versus contributions, as well as the endowments of the participants. Each treatment has a different level of contributions for each the dominant strategy equilibrium and the Pareto-optimal outcome.
Intervention Start Date
Intervention End Date
Primary Outcomes
Primary Outcomes (end points)
Do participants contribute at or near the dominant strategy equilibrium?
Do participants contribute at or near the Pareto-optimal outcome?
Primary Outcomes (explanation)
Secondary Outcomes
Secondary Outcomes (end points)
Do participants contribute more to the group in the presence of inequality in their favor ("guilt")?
Do participants contribute less to the group in the presence of inequality against them ("envy")?
Are there gender differences in contribution rates?
Do participants who contribute more in the charity dictator game also contribute more in the public goods game?
Secondary Outcomes (explanation)
Experimental Design
Experimental Design
Participants from an undergraduate pool will complete a series of tasks using custom computer software which provides detailed real-time feedback on the payoffs of their choices. They will go through a series of rounds; in each round, they will be randomly assigned to a group, given an endowment and asked to choose how much of that endowment to contribute to their group (a public goods game). Contributions to the group will be shared across participants with a marginal per-capita return between 0 and 1; endowments not contributed will then be "taxed" according to a rule explained to the participants. In some treatments tax revenue will have a marginal per-capita return higher than contribution; in others, lower. All treatments will be conducted using a within-participant design with randomized ordering. The dominant strategy equilibrium and the Pareto-optimal outcome will vary across treatments. A charity dictator task at the end will provide an independent measure of other-regarding preferences.
Experimental Design Details
Not available
Randomization Method
Randomization by computer
Randomization Unit
Sessions will be randomized into different treatment orderings, while individuals will be randomly assigned into new groups at each round.
Was the treatment clustered?
Experiment Characteristics
Sample size: planned number of clusters
12 sessions
Sample size: planned number of observations
240 participants
Sample size (or number of clusters) by treatment arms
3 sessions of each of 4 treatment orderings
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Effect size will be measured as mean deviation in contributions from the dominant strategy equilibrium. This sample size should be sufficient to detect an effect size of 0.5 or more as measured by Cohen's d, with 90% statistical power.
IRB Name
University of California, Irvine IRB C: Social and behavioral sciences
IRB Approval Date
IRB Approval Number