Primary Outcomes (end points)
We will test seven hypotheses.
1) A non-negligible percentage of first-movers give more in the influence scenario. We will estimate the percentage of first-movers who give more in the influence scenarios.
2) The proportion of first-movers who give more in the influence scenario is significantly larger than the proportion who give more in the no influence scenario. We will compare the proportion in both groups with a paired t-test.
3) First-movers who contribute more in the leadership scenario make the no influence scenario significantly more likely to be implemented than the influence scenario. We will estimate, among first-movers who contribute more in the leadership scenario, the proportion who make the no influence scenario more likely.
4) Consider first-movers who contribute the same amount in both contingencies. The higher their contribution, the more likely they are to make the influence scenario more likely. We will test for this by looking at the proportion of first-movers who make the influence contingency more likely, dividing the data by terciles. We will further test for this via an OLS regression, restricted to subjects who contributed the same amount in both scenarios, where the dependent variable is whether the subject made the influence contingency more likely to be implemented, and the independent variable is the first-mover's contribution.
5) Consider the following condition on the first-mover's beliefs: the first-mover believes that the second-mover will contribute more in the no influence scenario than he would in the influence scenario had the first-mover contributed the same amount in that scenario as in the no influence scenario. First-movers whose beliefs fulfill this condition are more likely to contribute more in the influence scenario and then make the no influence scenario more likely to be implemented. To test for this, we will run an OLS regression in which the independent variable is an indicator variable equal to one if the first-mover's beliefs fulfill the above condition, and the dependent variable is an indicator variable equal to one if the first-mover contributes more in the influence scenario and then makes the no influence scenario more likely to be implemented.
6) The difference in contributions between the influence and no influence scenarios increases with the social expectations in the influence scenario and decreases with social expectations in the no influence scenario. The first effect is stronger than the second. Social expectations are measured via first-movers' guesses over what other first-movers guessed first movers would do in each scenario. In order to test this hypothesis, we follow a difference in difference specification. The unit of analysis is a subject-scenario. That is, there are two observations per subject. We then are interested in a difference in difference regression where the variables that interact is the scenario the first-mover is in and the social expectation of a specific scenario. To be explicit, the main regressors are a dummy for the influence scenario, social expectations in the influence scenario, social expectations in the no influence scenario, the interaction between the dummy for the influence scenario and social expectations in the influence scenario, and the interaction of a dummy for the influence scenario and social expectations in the no influence scenario. The coefficients of interest are the interaction terms.
7a) First-movers who contribute the same amount in both scenarios will make the influence scenario more likely to be implemented under the following condition on beliefs: if the contribution they expect from second-movers in the no influence scenario is lower than the contribution they expect in the influence scenario. To test for this, we run an OLS regresson, restricted to first-movers who contributed the same in both scenarios, in which the dependent variable is an indicator variable equal to one if the first-mover makes the influence scenario more likely to be implemented, and the independent variable is an indicator variable equal to one if the condition on beliefs stated in this hypothesis hold.
7b) First movers who contribute the same amount in both scenarios are more likely to make the influence scenario more likely to be implemented if the following condition on beliefs holds: their contribution in the influence scenario is at least as high as their social expectations in that scenario. To test for this, we run an OLS regresson, restricted to first-movers who contributed the same in both scenarios, in which the dependent variable is an indicator variable equal to one if the first-mover makes the influence scenario more likely to be implemented, and the independent variable is an indicator variable equal to one if the condition on beliefs stated in this hypothesis hold. The regression includes as controls social expectations of the influence and no influence scenarios.