Experimental Design
Treatments
Our experiment employs a between-subject design. In each treatment, subjects participate in the public goods game with either symmetric or asymmetric MPCRs. In order to examine whether subjects’ contributions to the public goods depend on others’ contributions in their group or the opposing group, we use the strategy method developed in FGF (2001), where players make both unconditional and conditional contributions. Subjects are asked to complete three tasks: first, an unconditional contribution task where subjects simply play the public goods game as the model describes; second, a conditional contribution task, in which subjects need to make contribution decisions given each possible situation of others’ contributions in their group and in the opposing group; finally, subjects are asked to complete a survey.
In the conditional contribution task, the subjects are shown a “contribution table,” where each row presents the number of tokens contributed by other members in their own group (named as own-group contribution) and by members in the opposing group (named as other-group contribution). The subjects need to decide whether to contribute to their own group account for each row. The conditional contribution table is presented by ordering others’ contributions from the lowest to the highest. However, different from FGF (2001), since we have two subgroups, we face a choice of whether to list the first column in the contribution table as others’ contribution from one’s own group (referred as Framework 1) or from the opposing group (referred as Framework 2). We conduct treatments for both frameworks to mitigate any potential framework effect.
In summary, our experiment employs a 2×2 design. We denote treatment 1 as T1 (SymFrame1) for symmetric MPCR combined with framework 1. T2 (AsymFrame1), T3 (SymFrame2), and T4 (AsymFrame2) follow the same notation rule.
Experimental Procedure
The experiment was conducted on the platform Amazon Mechanical Turk (MTurk). The public goods game was programmed using oTree (Chen, Schonger, & Wickens, 2016). In each treatment, each participant was randomly assigned to one of the two roles, A (majority) or B (minority), and the role remains the same through the experiment. In all the four treatments, the subjects play the game only once.
All sessions began with a consent form, followed by the instructions for Task 1 (unconditional contribution), quiz questions, and the decision for Task 1. After completing Task 1, the subjects proceeded with the instructions and decisions in Task 2 (conditional contribution) and Task 3 (a post-experiment survey). Detailed instructions can be found in Appendix C.
Task 1:
The “unconditional contribution” was a single decision about whether or not to invest the token into the public good. In the instructions, the subjects were given the payoff function that represents the public goods model with polarized preferences, as well as examples of how to calculate the payoffs. They were told that there were two types (groups) of players, role A and role B, and the role would not change for the entire session.
Task 2:
The “conditional contribution” followed a similar procedure in FGF (2001) except that we incorporated the polarized preferences. Specifically, subjects were shown a “contribution table” which contains all the possible combinations of the tokens in the two group accounts. For a subject in group A, there were 24 (6x4) rows (decisions) in the table. Each row represented a possible contribution from other members in group A (0 to 5), combined with a possible contribution from members in group B (0 to 3). Similarly, for a subject in group B, there were 21 (3x7) rows in the table, with the possible contribution from other members in group B ranging from 0 to 2 and in group A ranging from 0 to 6.
Task 3:
The survey task included five preference questions on positive and negative reciprocity, trust, risk, and altruism, which were modified from Falk et al. (2023), three CRT questions, demographic questions on age, gender, and ethnicity as well as an open comment.
All tasks were performed only once, which was made clear to subjects at the beginning of each session. Using a strategy method, we conducted the session for player A and player B separately for each treatment. Each subject made decisions individually and independently, without receiving feedbacks on other participants' decisions during the experiment. For each treatment, after all role-A players and role-B players submitted the tasks, we randomly assigned subjects to groups according to the designed group size (6A vs. 3B) and calculated the bonus payoffs for each player.
Subjects were paid bonus payoffs for the three tasks, as well as a base rate for the completion of the experiment. We determined subjects’ bonus payoff from Task 1 and Task 2 by using a similar method as in FGF (2001). For each group, one subject out of nine was randomly selected, whose contribution table would be the payoff-relevant decision. For the other eight participants who were not selected, only the unconditional contribution table would be the payoff-relevant decision. Subjects did not know whether the random mechanism would select him/her when making decisions, so they would have to think carefully about both unconditional and conditional tasks.
Theoretically, subjects may earn a negative payoff from the public goods game due to the polarized preferences. We compensated the subjects with a constant amount in Task 3 to guarantee that the total bonus payoff from the three tasks in each treatment is at least 1 token. Subjects, however, were only informed about the amount of the bonus payoff for Task 3 when they reached that stage. The experimental money was converted to US dollars with an exchange rate of 1 token = $1.0.