A positive Shapley value means that all players decide to contribute (if basing their decisions off Shapley values as advocated in this post), and you then end up with N=3
Since I was calculating the Shapley value relative to doing nothing, it being positive only means taking the action is better than doing nothing. In reality, there will be other options available, so I think agents will want to maximise their Shapley cost-effectiveness. For the previous situation, it would be:
SCE(N)=1−(1−p)NNVc.
For the previous values, this would be 7⁄6. Apparently not very high, considering donating 1 $ to GWWC leads to 6 $ of counterfactual effective donations as a lower bound (see here). However, the Shapley cost-effectiveness of GWWC would be lower than their counterfactual cost-effectiveness… In general, since there are barely any impact assessments using Shapley values, it is a little hard to tell whether a given value is good or bad.
Since I was calculating the Shapley value relative to doing nothing, it being positive only means taking the action is better than doing nothing. In reality, there will be other options available, so I think agents will want to maximise their Shapley cost-effectiveness. For the previous situation, it would be:
SCE(N)=1−(1−p)NNVc.
For the previous values, this would be 7⁄6. Apparently not very high, considering donating 1 $ to GWWC leads to 6 $ of counterfactual effective donations as a lower bound (see here). However, the Shapley cost-effectiveness of GWWC would be lower than their counterfactual cost-effectiveness… In general, since there are barely any impact assessments using Shapley values, it is a little hard to tell whether a given value is good or bad.