Experimental Design Details
The group task in stage 1 follows the ‘Wordfind game’ proposed by Laura A. Dabbish (2008). We conducted a manipulation test of the group task in June 2019. Utilizing the IOS (Aron, 1992) and IIS (Tropp & Wrights, 2001) after the group task, the pretest shows that participants feel significantly closer to individuals who were previously part of the same group than to individuals who were part of a different group (p = 0.01). Likewise, individuals who are matched with new group members feel less close to the new group than individuals who stay in the same group (p = 0.03).
In stage 2 participants bargain over the distribution of 24 payoff points 8 times consecutively. The sum of the assigned thresholds always add up to 15, but each round the inequality of thresholds between the same three participants increases within the treatments. I.e.:
- Round 1: 5 - 5 - 5
- Round 2: 4 - 5 - 6
- Round 3: 3 - 5 - 7
- Round 4: 2 - 5 - 8
- Round 5: 1 - 5 - 9
- Round 6: 0 - 5 - 10
- Round 7: 0 - 3 - 12
- Round 8: 0 - 1 - 14
Round 1 is independent of previous outcomes and, hence, allows an independent, statistically sound comparison between the treatments. Rounds 2 - 8 can be affected by the new thresholds levels, but also by learning, experience (effect of previous bargaining outcomes, e.g. reciprocity), and overarching strategic considerations (e.g., fairness). To minimize the influence of experience and meta-strategies on the bargaining outcomes, we pay only one round, which is randomly selected after the experiment. To minimize the influence of learning on the bargaining outcomes we randomize round 2-8, which in theory should entail the same average learning effects across the different rounds. We argue this ensures the best design given the restriction that we can only conduct a limited number of between-subject treatments due to a limited subject pool.
The real effort task in stage 3 consists of a weighted mix between math puzzles, word finding games and trivia questions. We do not provide information about the difficulty of the tasks, nor the average payoff from the tasks. However, we ask about the expected payoff from the tasks for oneself and others.
We test the following hypotheses:
- Hypothesis 1: NSR-G of treatment 3 is higher than in the control treatment, treatment 1 and 2.
- Hypothesis 2: The higher the inequality of need thresholds, the lower the NSR-G.
- Hypothesis 3a: Within treatment 2, subjects who played together in stage 1 are more likely to form coalitions in stage 2 than subjects who did not.
- Hypothesis 3b: Within treatment 2, subjects who played together in stage 1 are more likely to satisfy their need thresholds in stage 2 than the need thresholds of subjects who did not.
- Hypothesis 4: The more rounds the groups play in stage 2, the less effective are the induced differences of the social relationship in stage 1.